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The additive inverse of a vector equals the vector multiplied by -1.
The additive inverse of a vector is called the negative of the vector.
The additive inverse of a vector is unique.
The adjoint of a matrix-scalar product is the product of the adjoint and the conjugate.
The adjoint of a product of matrices is the product of the adjoints in reverse order.
The adjoint of a sum is the sum of the adjoints.
The Cauchy-Schwartz inequality
The Cauchy-Schwarz inequality
The Cayley-Hamilton theorem for a linear transformation
The Cayley-Hamilton theorem for a matrix.
The change of coordinates matrix between two bases exists and is unique
The characteristic polynomial applied to the matrix gives the 0 matrix.
The column space of a matrix is a vector space
The column space of an m-by-n matrix is a subspace of R^m (or C^m)
The composition of injective linear transformations is injective
The composition of invertible linear transformations is invertible
The composition of linear transformations is a linear transformation
The composition of surjective linear transformations is surjective
The condition number of matrix measures how close it is to being singular
The conjugate of a matrix-scalar product is the product of the conjugates.
The conjugate of a product of matrices is the product of the conjugates.
The conjugate of a sum of vectors in C^n is the sum of the conjugates
The conjugate of the sum of matrices is the sum of the conjugates.
The conjugate of the transpose is the transpose of the conjugate.
The conjugate of vector-scalar multiplication in C^n is the product of the conjugates.

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