Theorems · Theorem · linear algebra

Matrix.ext_iff_trace_mul_left

∀ {m : Type u_2} {n : Type u_3} {R : Type u_6} [inst : Fintype m] [inst_1 : Fintype n] [inst_2 : NonAssocSemiring R]
  {A B : Matrix m n R}, A = B ↔ ∀ (x : Matrix n m R), (x * A).trace = (x * B).trace

Matrices A and B are equal iff (x * A).trace = (x * B).trace for all x.

Defined in

Mathlib.LinearAlgebra.Matrix.Trace

Cited by

0 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeFintypeNonAssocSemiring