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- The complex inner product is conjugate symmetric#23898
- The composition of injective linear transformations is injective#24025
- The composition of invertible linear transformations is invertible#24027
- The composition of linear transformations is a linear transformation#24024
- The composition of surjective linear transformations is surjective#24026
- The conjugate of a matrix-scalar product is the product of the conjugates.#23468
- The conjugate of a product of matrices is the product of the conjugates.#23469
- The conjugate of a sum of vectors in C^n is the sum of the conjugates#23791
- The conjugate of the sum of matrices is the sum of the conjugates.#23467
- 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