A non-commutative algorithm for multiplying (7 $\times$ 7) matrices using 250 multiplications

Alexandre Sedoglavic (CRIStAL)

RECORD

A non-commutative algorithm for multiplying (7 $\times$ 7) matrices using 250 multiplications

Alexandre Sedoglavic (CRIStAL)

Symbolic Computation · Submitted 21 Dec 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We present a non-commutative algorithm for multiplying (7x7) matrices using 250 multiplications and a non-commutative algorithm for multiplying (9x9) matrices using 520 multiplications.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

arXiv ID1712.07935 (version 1)

Pith IDWFDTGFXF, Pith's permanent record of this paper and its review

CitationAlexandre Sedoglavic (CRIStAL). "A non-commutative algorithm for multiplying (7 $\times$ 7) matrices using 250 multiplications." arXiv:1712.07935 (2017). https://pith.science/paper/WFDTGFXF

Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,292 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.14 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.09 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We present a non-commutative algorithm for multiplying (7x7) matrices using 250 multiplications and a non-commutative algorithm for multiplying (9x9) matrices using 520 multiplications. These algorithms are obtained using the same divide-and-conquer technique.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We present a non-commutative algorithm for multiplying (7x7) matrices using 250 multiplications and a non-commutative algorithm for multiplying (9x9) matrices using 520 multiplications.	contribution 0.82	0.94	0.87	asserted 1.00
s1	These algorithms are obtained using the same divide-and-conquer technique.	method 1.00	0.84	0.06	asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.99 · evidence from proof or derivation 0.97.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We present a non-commutative algorithm for multiplying (7x7) matrices using 250 multiplications and a non-commutative algorithm for multiplying (9x9) matrices using 520 multiplications. These algorithms are obtained using the same divide-and-conquer technique.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

4 arXiv papers cite this in 5 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 3 sentences without a confident label

Uses its data or values 1 paper

For $n=7$, [ref] found a way to compute the product with 250 multiplications.

New ways to multiply 3 x 3-matrices · Introduction · 0.80

Cites it as background 1 paper

Extensive background in this direction is available in [ref] , and some known upper bounds for $R(p,m,n)$ can be found in [ref] .

Private and Secure Distributed Matrix Multiplication Schemes for Replicated or MDS-Coded Servers · Comparison · 0.99

What it cites · 3 sentences without a confident label

Uses data or values from 1 paper

Again, we found in [ref] that $⟨3,3,6⟩=40$ (an explicit form of this algorithm could be found in the source code of [ref] or in the collection [ref] ).

A Framework for Practical Parallel Fast Matrix Multiplication · An algorithm for multiplying $99$ matrices · 0.89

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.