Theorems · Theorem · linear algebra
Matrix.fromCols_mul_fromRows
∀ {R : Type u_1} {m : Type u_2} {n : Type u_5} {n₁ : Type u_6} {n₂ : Type u_7} [inst : Semiring R] [inst_1 : Fintype n₁]
[inst_2 : Fintype n₂] (A₁ : Matrix m n₁ R) (A₂ : Matrix m n₂ R) (B₁ : Matrix n₁ n R) (B₂ : Matrix n₂ n R),
A₁.fromCols A₂ * B₁.fromRows B₂ = A₁ * B₁ + A₂ * B₂A column partitioned matrix multiplied by a row partitioned matrix gives the sum of the "outer" products of the block matrices.
- Defined in
- Mathlib.Data.Matrix.ColumnRowPartitioned
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
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- Semiringstatement and proof · cited by 13,802
- Fintypestatement and proof · cited by 7,736
- Finset.sumproof · cited by 5,195
- Matrixstatement and proof · cited by 4,303
- Finset.univproof · cited by 3,473
- Matrix.extproof · cited by 540
- Matrix.fromRowsstatement and proof · cited by 35
- Matrix.fromColsstatement and proof · cited by 30
- Fintype.sum_sum_typeproof · cited by 22
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