Linear Algebra

Contents

Matrices, Vectors: Addition and Scalar Multiplication, Matrix Multiplication, Linear Systems of Equations, Gauss Elimination, Linear Independence, Rank of a Matrix, Vector Space, Solutions of Linear Systems: Existence, Uniqueness, Determinants, Cramer's Rule, lnverse of a Matrix, Gauss-Jordan Elimination , Vector Spaces, Inner Product Spaces. Linear Transformations, Matrix Eigenvalue Problem, Determining Eigenvalues and lSigenvectors, Some Applications of Eigenvalue Problems, Matrix representation and sums and products of linear operators, The range and null space of linear operators, lnvariant subspaces, Transformation to new bases and consecutive transformations, Transformations of the matrix of a linear operator, Canonical form of the matrix of a nilponent operator, Polynomial algebra and canonical form of the matrix of an arbitrary operator