[Merged by Bors] - feat: Invertible matrices #8219
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| simp_rw [vecMul_transpose] | ||
| exact LinearMap.surjective_of_injective (f := A.mulVecLin) h | ||
| change Function.Injective A.mulVecLin | ||
| rw [←LinearMap.ker_eq_bot, LinearMap.ker_eq_bot'] |
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| rw [←LinearMap.ker_eq_bot, LinearMap.ker_eq_bot'] | |
| rw [← LinearMap.ker_eq_bot, LinearMap.ker_eq_bot'] |
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Is there a style guide reference for having the space after the arrow?
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And if it's part of the official style, why doesn't the linter enforce it?
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We add some results on invertible matrices, showing that for a finite square matrix `A`, `IsUnit A` is equivalent to the surjectivity/injectivity of left/right multiplication, and to the linear independence of the set of rows/columns. We also add a couple of lemmas about the existence of left/right inverses for nonsquare matrices, and a bit of API for `mulVecLin` and `vecMulLinear`. Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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We add some results on invertible matrices, showing that for a finite square matrix `A`, `IsUnit A` is equivalent to the surjectivity/injectivity of left/right multiplication, and to the linear independence of the set of rows/columns. We also add a couple of lemmas about the existence of left/right inverses for nonsquare matrices, and a bit of API for `mulVecLin` and `vecMulLinear`. Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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We add some results on invertible matrices, showing that for a finite square matrix
A,IsUnit Ais equivalent to the surjectivity/injectivity of left/right multiplication, and to the linear independence of the set of rows/columns.We also add a couple of lemmas about the existence of left/right inverses for nonsquare matrices, and a bit of API for
mulVecLinandvecMulLinear.