Theorems · Theorem · linear algebra
Matrix.star_vec_dotProduct_vec
∀ {m : Type u_2} {n : Type u_3} {R : Type u_1} [inst : AddCommMonoid R] [inst_1 : Mul R] [inst_2 : Star R]
[inst_3 : Fintype m] [inst_4 : Fintype n] (A B : Matrix m n R), star A.vec ⬝ᵥ B.vec = (A.conjTranspose * B).trace- Defined in
- Mathlib.LinearAlgebra.Matrix.Vec
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Star.starstatement and proof · cited by 1,082
- Starstatement and proof · cited by 496
- Matrix.mapproof · cited by 247
- Matrix.conjTransposestatement and proof · cited by 202
- dotProductstatement · cited by 194
- Matrix.tracestatement and proof · cited by 114
- Matrix.transpose_transposeproof · cited by 33
- Matrix.vecstatement · cited by 27
- Matrix.vec_dotProduct_vecproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.trace_conjTranspose_mul_self_eq_zero_iffproof · cited by 1