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- The conjugate of the transpose is the transpose of the conjugate.#23505
- The conjugate of vector-scalar multiplication in C^n is the product of the conjugates.#23793
- The coordinate vector relative to a given basis is a linear mapping to R^n (or C^n).#23992
- The coordinate vector relative to a given basis is an injective linear mapping to R^n (or C^n).#23993
- The coordinate vector relative to a given basis is a surjective linear mapping to R^n (or C^n).#23994
- The crazy vector space is a vector space.#24107
- The determinant function exists.#23734
- The determinant function is unique.#23735
- The determinant of a block diagonal matrix is the product of the determinants of the blocks.#23731
- The determinant of a matrix can be computed as a cofactor expansion across any row.#23719
- The determinant of a matrix can be computed as a cofactor expansion down any column.#23720
- The determinant of a matrix can be expressed as a product of the diagonal entries in a non-scaled echelon form.#23725
- The determinant of a matrix measures the area/volume of the parallelogram/parallelipiped determined by its columns.#23746
- The determinant of a triangular matrix is the product of the entries on the diagonal.#23744
- The determinant of the inverse of A is the reciprocal of the determinant of A.#23730
- The determinant of the matrix of a linear transformation is the factor by which the area/volume changes.#23747
- The dimension of a direct sum of subspaces is the sum of the dimensions of the subspaces.#23971
- The dimension of a eigenspace is less than or equal to the (algebraic) multiplicity of the eigenvalue.#23708
- The dimension of a subspace is less than or equal to the dimension of the whole space#24010
- The dimension of the domain of an injective linear transformation is at most the dimension of the codomain.#24033
- The dimension of the domain of a surjective linear transformation is at least the dimension of the codomain.#24034
- The direct sum of a subspace and its orthogonal complement is the whole space.#23922
- The echelon form can be used to determine if a linear system is consistent.#23771
- The eigenspace of a linear transformation is a nontrivial subspace.#24051
- The eigenvalues of a matrix are the roots/solutions of its characteristic polynomial/equation.#23705
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