- - generic Vector Space
- - generic vector of .
- - Vector addition
- - scalar multiplication between
- - either the zero vector or the zero scalar (depending on context)
- - is a subspace of
- - sum of subspaces
- - direct product of two subspaces
- - the zero subspace
- - vector spaces and are isomorphic
- - a generic matrix
- - the entry in matrix at the -th row
- - the entry in matrix at the -th column
- - the entry in matrix at the -th row and -th column
- - the transpose of
- - the inverse of
- - Kronecker sum of two matrices
- - Kronecker product of two matrices
- - trace of
- - vector space of -tuples over field
- - vector space of all matrices over field .
- - the set of all functions from into .
- - the set of all linear transformations from to .
- - zero matrix
- - identity matrix (of order )
- - change of coordinate basis
- - compact notation for the diagonal matrix constructed by using the entries of the vector .
- - span of set
- - basis vector
- - dimension of .
- - coordinate vector of in terms of basis
- - standard representation of vector space with respect to basis .
- - generic linear transformation
- - identity transformation from to
- - zero transformation
- - null space of
- - column space of
- - nullity of
- - rank of
- - the matrix associated with the linear transformation where and are the bases for and respectively
- - left multiplication transformation using matrix .
- - inverse of linear transformation .
- - similar matrices
- - the restriction of on .
- - the dual space of .
- - the dual basis of .
- - the annihilator of
- - the determinant of .
- - generic eigenvalue of or .
- - the spectrum of . That is, the set of its eigenvalues.
- - generic diagonal matrix consisting of eigenvalues in an eigendecomposition.
- - generic characteristic polynomial
- - eigenspace corresponding to
- - algebraic multiplicity of under the linear transformation .
- - geometric multiplicity of under the linear transformation (or matrix )
- - the - cyclic subspace generated by .
- - the -cyclic basis of
- - The limit of the sequence of matrices is
- - sum of absolute values of row of .
- - sum of absolute values of column of .
- - row sum
- - column sum
- - the inner product of and .
- - standard inner product / dot product of and .
- - standard inner product of and in .
- - complex conjugate of
- - adjoint of linear transformation
- - conjugate transpose of matrix
- - norm of vector .
- - norm of matrix
- - distance between and
- - orthogonal complement of .
- - orthogonal projection of .
- - generic bilinear form
- - the set of all bilinear forms on .
- - the matrix representation of bilinear form with respect to basis .
- - generic quadratic form
- - index of a real symmetric matrix
- - canonical form of a symmetric matrix with index and rank .
- - Rayleigh quotient
- - condition number of .
- - generic Jordan block
- - generalized eigenspace corresponding to .
- - generic cycle of generalized eigenvectors