Systems of linear equations, Gauss elimination method, Reduced Echelon form, describing solution sets.
Vector spaces: subspaces, linear independence, spanning, bases, dimension.
Linear transformations, kernel and image
Matrices, determinants, conjugate matrices, inverse of a matrix, transpose.
Eigenvalues, eignevectors, characteristic polynomial, diagonalization of matrices.
Cayley-Hamilton theorem, minimal polynomial
Inner products, symmetric and orthogonal matrices, self-adjoint and unitary transformations.