Paper Citation Record · LEDGER

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition

As of 16 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 0 inbound Pith citation observations for arXiv:1908.09326.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
1908.09326 v1

Coverage vector

measured 41 of 41 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T11:24:31.840488Z

measured 41 of 41 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

41 of 41 outbound references displayed

verified exact0
verified fuzzy28
unresolved12
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 2381a303-8d11-4b0f-8294-54f86e9a6da6 · outbound

This paper cites Aftab and R.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Aftab and R

Reference 1

Resolution: malformed identifier; raw_fallback, observed 2026-08-14T11:24:32.272844Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 78057ddd-1e67-416e-9810-17482c9058d5 · outbound

This paper cites Ando, C.-K.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Ando, C.-K

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:32.262134Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a5422df3-6292-413a-a250-64f7d7e76fd5 · outbound

This paper cites Arnaudon, F.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Arnaudon, F

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:32.251710Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 2c1ee2a6-b1dc-4073-b077-b75c5a4ebd75 · outbound

This paper cites Arsigny, P.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Arsigny, P

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:32.241786Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 3d8575b9-3ea1-4807-af37-6dace6ddc409 · outbound

This paper cites Barachant, S.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Barachant, S

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:32.232361Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 448f7cff-2560-46ab-b869-24cf0ed71491 · outbound

This paper cites Bhatia, Positive Deﬁnite Matrices , Princeton University Press, 2007.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Bhatia, Positive Deﬁnite Matrices , Princeton University Press, 2007

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:32.222911Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation d879d135-d909-47ba-a2db-51530ea94160 · outbound

This paper cites Bhatia, T.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Bhatia, T

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:32.213283Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 4867b09d-0b6b-44fb-9920-c2bb3ac4e427 · outbound

This paper cites Bhattacharya and V.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Bhattacharya and V

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:32.203788Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 05f3fad1-2503-47be-ae80-c8f5a93a6ee4 · outbound

This paper cites Caseiro, J.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Caseiro, J

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:32.193838Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation fef6a838-9405-477f-95da-30705dd2640d · outbound

This paper cites Chebbi and M.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Chebbi and M

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:32.184022Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 9b85dbc7-95e6-4dde-a685-fe4124d7fc7e · outbound

This paper cites an unresolved cited work.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-14T11:24:32.173798Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 9b9f1583-934e-4728-9bc9-2dd5d05720cf · outbound

This paper cites an unresolved cited work.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-14T11:24:32.163789Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 9fc56760-b198-4006-a64a-e2b718b52221 · outbound

This paper cites Fillard, V.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Fillard, V

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:32.153954Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 97cf1272-4bf8-41a1-881f-8ea1454619fc · outbound

This paper cites an unresolved cited work.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-14T11:24:32.145379Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a7cecd73-e68d-4573-9cce-2838fff6b90c · outbound

This paper cites an unresolved cited work.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-14T11:24:32.136299Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 23564ddc-22ef-4c9c-a29e-08afc2f833c8 · outbound

This paper cites an unresolved cited work.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-14T11:24:32.126658Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 9c29bd02-2b5f-4595-bfe3-cfb152e7f377 · outbound

This paper cites Grubiˇsi´c and R.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Grubiˇsi´c and R

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:32.116880Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation e82ba16c-ad61-43ac-9b6f-3de3b13ee1b8 · outbound

This paper cites Guilleminot and C.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Guilleminot and C

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:32.106354Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 0af2c8ab-f0da-4708-91b9-245048940d0a · outbound

This paper cites Helgason, Diﬀerential Geometry, Lie Groups, and Symmetric Spaces , American Mathe- matical Society, 2001.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Helgason, Diﬀerential Geometry, Lie Groups, and Symmetric Spaces , American Mathe- matical Society, 2001

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:32.096460Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 1cfef4a7-ae88-41de-9981-f7303b17daac · outbound

This paper cites Hosseini and S.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Hosseini and S

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:32.086297Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 0db70219-5957-402a-b07f-0b5d80d2f0f6 · outbound

This paper cites an unresolved cited work.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-14T11:24:32.077185Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation fe365222-8eda-4a61-be3c-c552a18b6d2d · outbound

This paper cites an unresolved cited work.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-14T11:24:32.067495Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation fa5c8164-8f08-4d3e-be98-070e6c34ad05 · outbound

This paper cites an unresolved cited work.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-14T11:24:32.058662Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ff2c6a8d-90c2-4180-9170-6fd427428131 · outbound

This paper cites Lang, Diﬀerential and Riemannian Manifolds , Springer, New York, 1995.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Lang, Diﬀerential and Riemannian Manifolds , Springer, New York, 1995

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:32.049419Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 5148d665-d0f4-4cfe-ab52-7d25a410ba34 · outbound

This paper cites Le Bihan , Molecular diﬀusion nuclear magnetic resonance imaging , Magnetic Resonance Quarterly, 7 (1991), pp.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Le Bihan , Molecular diﬀusion nuclear magnetic resonance imaging , Magnetic Resonance Quarterly, 7 (1991), pp

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:32.039325Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a5e68e61-5eb6-4ac3-98ec-b0b3a66460c2 · outbound

This paper cites an unresolved cited work.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-14T11:24:32.029116Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation db14b82f-f129-4c00-8830-ecb1c23b4e9f · outbound

This paper cites Lenglet, M.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Lenglet, M

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:32.018639Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation eb09b852-5672-4b7e-a711-eef8e282fdcf · outbound

This paper cites Massart and P.-A.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Massart and P.-A

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:32.008352Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 6aaa07cc-fe27-4c0a-980c-a556c7736b23 · outbound

This paper cites Milnor, Morse Theory, Princeton University Press, 1963.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Milnor, Morse Theory, Princeton University Press, 1963

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:31.997330Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 5f7fd5aa-2b3e-4ac5-a3a5-0bfe2a134eff · outbound

This paper cites Moakher, A diﬀerential geometry approach to the geometric mean of symmetric positive- deﬁnite matrices, SIAM Journal on Matrix Analysis and Applications, 26 (2005), pp.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Moakher, A diﬀerential geometry approach to the geometric mean of symmetric positive- deﬁnite matrices, SIAM Journal on Matrix Analysis and Applications, 26 (2005), pp

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:31.986238Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 3d8cb7ac-615d-44e9-8075-c14fc8ee20a4 · outbound

This paper cites Moakher, On the averaging of symmetric positive-deﬁnite tensors , Journal of Elasticity, 82 (2006), pp.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Moakher, On the averaging of symmetric positive-deﬁnite tensors , Journal of Elasticity, 82 (2006), pp

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:31.976054Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 06d5db5e-6d8e-40a1-a149-4b10d84ee485 · outbound

This paper cites Osborne, V.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Osborne, V

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:31.965680Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a05bfc3f-1b7a-4aff-ab3f-d4c7fcde94fd · outbound

This paper cites Pennec, Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measure- ments, Journal of Mathematical Imaging and Vision, 25 (2006), pp.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Pennec, Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measure- ments, Journal of Mathematical Imaging and Vision, 25 (2006), pp

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:31.955097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 5bf59424-6f61-4ba4-8816-6e77c2d86198 · outbound

This paper cites Pennec, P.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Pennec, P

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:31.944281Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 9c6f244f-1c90-469c-9984-adf0001de248 · outbound

This paper cites Rathi, A.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Rathi, A

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:31.934931Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation cb5ec74f-1199-4471-9f64-da5bfc7ba958 · outbound

This paper cites Schiratti, S.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Schiratti, S

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:31.923656Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 12a48fbe-5c7d-4a22-8089-f40a4f38e5f4 · outbound

This paper cites Sra, Positive deﬁnite matrices and the S-divergence , Proceedings of the American Mathe- matical Society, 144 (2016), pp.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Sra, Positive deﬁnite matrices and the S-divergence , Proceedings of the American Mathe- matical Society, 144 (2016), pp

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:31.912459Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation c1d5ad96-9957-46bb-a293-4aa672734a92 · outbound

This paper cites Vandereycken, P.-A.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Vandereycken, P.-A

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:24:31.901902Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 8fecbdf1-580f-4ca6-9833-b514f3ff6992 · outbound

This paper cites an unresolved cited work.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Unresolved cited work

Reference 39

Resolution: unresolved; raw_fallback, observed 2026-08-14T11:24:31.891873Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a0ad30d8-19f9-4e86-8385-7b145e58f280 · outbound

This paper cites an unresolved cited work.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Unresolved cited work

Reference 40

Resolution: unresolved; raw_fallback, observed 2026-08-14T11:24:31.881859Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 018e5a56-e585-41bd-ad52-2483791d55da · outbound

This paper cites an unresolved cited work.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition Unresolved cited work

Reference 41

Resolution: unresolved; raw_fallback, observed 2026-08-14T11:24:31.871827Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Pith citing papers

No inbound Pith citation observations are available.