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Let $p , q $ be nonzero natural numbers and let $\\mu =( [m_{i,j}, M_{i,j}])_{i,j}$ be a $p \\times q$ interval matrix; given a $p \\times q$ matrix $A$ with entries in the set of real numbers, we say that $ A \\in \\mu $ if $a_{i,j} \\in [m_{i,j}, M_{i,j}] $ for any $i,j$. We establish a criterion to say if an interval matrix contains a matrix of rank $1$. Moreover we determine the maximum rank of the matrices contained in a given interval matrix. Finally, for any interval matrix $\\mu$ with no more than $3$ colum"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1712.09940","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-12-28T17:16:37Z","cross_cats_sorted":[],"title_canon_sha256":"2777f1deaa3a1caac9233961507d89506120037efe0ea0920cf7bb938e0a5042","abstract_canon_sha256":"b5a8b95cdaa320f5a3a6b88102a3e3ee9851573c7ecca82e78af8c9fb69df55a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:15.718401Z","signature_b64":"8msmX+GOGPR07vti8aRNbQDZp7u5ML0q1aKRTeaDRh0vkV3oNveF93ld73FEcF6MoFbMYfLlUBziXIup8xDKCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1838519ec0076acb294f5af403811872682fcf28ad50ce8f26bdf084ebc9192e","last_reissued_at":"2026-05-18T00:22:15.717836Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:15.717836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On rank range of interval matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Elena Rubei","submitted_at":"2017-12-28T17:16:37Z","abstract_excerpt":"An interval matrix is a matrix whose entries are intervals in the set of real numbers. 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