HUJI2023/24

vector length and direction, vector operations, lines and planes, projection onto a line, complex vectors, length and inner product for complex vectors

matrix operations, matrix equations:, matrix multiplication, matrix inverse, special types of matrices (diagonal, symmetric, triangular, identity, orthogonal, normal matrices), complex matrices, Hermitian transpose, special types of complex matrices, properties of the Hermitian transpose operation

Gauss–Jordan elimination, reduced row echelon form (solving equations, augmented matrix, row operations), number of solutions, geometric interpretation (lines in two dimensions + planes in three dimensions), matrix equations, matrix inverse (using row operations, using elementary matrices), LU decomposition

vector spaces, vector spaces techniques (null space and kernel will be covered in chapter 5), abstract vector spaces

finding matrix representations, coordinate projections (particularly – change of basis), change of basis for matrices

abstract inner product spaces, projections, Gram–Schmidt orthogonalization, orthogonal and positive matrices, complex inner product spaces, inner product for complex vectors

Determinants

These links include the algebraic definition of the determinant and proofs of its properties

Eigenvalues and Eigenvectors

Theoretical linear algebra, nilpotent matrix