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Matrix overhaul#1935

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lowasser wants to merge 22 commits into
UniMath:masterfrom
lowasser:matrix-ops
Draft

Matrix overhaul#1935
lowasser wants to merge 22 commits into
UniMath:masterfrom
lowasser:matrix-ops

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@lowasser
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DO NOT SUBMIT: to be broken up into several smaller PRs; this PR exists to prototype the entire whole and to show the long-term goal of the sub-PRs.

This PR:

  • renames the existing tuple-based matrix concept to "grid"
  • defines a "matrix" concept around finite sequences instead of tuples
  • gets addition and scalar multiplication on matrices "for free" from the dependent product of modules (one of several reasons to use finite sequences)
  • defines square matrices, diagonal matrices, and identity matrices
  • defines matrix multiplication and shows its properties (which never happened for the original tuple-based matrix concept)
  • shows that square matrices on commutative rings form a unital associative algebra

That's probably enough to start with; matrix similarity, diagonalizability, determinants, traces, and more can come next...

@lowasser lowasser mentioned this pull request May 26, 2026
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