21MAT116 LINEAR ALGEBRA MATHEMATICS PAPER – II-

Unit I-

Matrices: Determinant and inverse of a matrix, Trace and Transpose, Determinants, Symmetric and Skew Symmetric Matrices, Hermitian and Unitary matrices, System of linear equations, consistency and solutions by Guess methods.

Unit II-

Vector Spaces: Real Vector spaces, Sub spaces, Linear independence, Coordinates and Basis, Dimension, Change of Basis, Row Space, Column Space and Null Space, Rank and Nullity.

Unit III-

Inner Product Spaces: Inner products, Orthogonality, Gram Schmidt Process, QR Decomposition, Best Approximation, Least Squares.

Unit IV-

Eigen values and Eigen vectors: Problems in Eigen Values and Eigen Vectors, Diagonalization, Orthogonal Matrices, Orthogonal Diagonalization, Quadratic Forms.

Unit V-

Linear Transformations: General Linear Transformations, Relation between matrices and linear transformations, Kernel and range of a linear transformation, Isomorphisms, Compositions and Inverse Transformations, Matrices for General Linear Transformations, Similarity.