|
Content
|
Matrices and Systems of Equations: Systems of Linear Equations, Row Echelon Form, Matrix algebra, elementary matrices, separated matrices, Determinants: determinant of a matrix, properties of determinant, Cramer`s rule, Vector spaces: definition and examples, subspaces, linear dependence, Base and dimension, base change, row space and column space, Linear transformations: definition and examples, matrix representation of linear representations, similarity, Orthogonality: scalar product in n-dimensional real space, orthogonal subspaces, Least squares method, inner product spaces, orthonormal sets, Gram-Shmidt orthogonalization process, orthogonal polynomials, Eigenvalues and eigenvectors, diagonalization, Hermit matrices, single value decomposition, Quadratic forms, Positive defined matrices
|