Theorems · Theorem · combinatorics
Matrix.IsHadamard.star_det_mul_det
∀ {n : Type u_2} {R : Type u_3} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommRing R] [inst_3 : StarRing R]
{A : Matrix n n R}, A.IsHadamard → star A.det * A.det = ↑(Fintype.card n) ^ Fintype.card nThe Hadamard determinant identity: star (det A) * det A = (card n)^(card n).
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- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
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- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- mul_commproof · cited by 2,262
- StarRingstatement and proof · cited by 1,686
- Fintype.cardstatement and proof · cited by 1,386
- Star.starstatement and proof · cited by 1,082
- Matrix.detstatement and proof · cited by 665
- Matrix.IsHadamardstatement and proof · cited by 24
- Matrix.IsHadamard.det_mul_star_detproof · cited by 3
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