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THEORY OF MATRICES of ULZ0027 covers the latest syllabus prescribed by General for All University for regulation 2016. Author uLektz, Published by uLektz Learning Solutions Private Limited.
Topics
1. Real matrices – Symmetric, skew – symmetric, orthogonal
2. Complex matrices: Hermitian, Skew- Hermitian and Unitary Matrices
3. Idempotent matrix, Elementary row and column transformations- Elementary matrix, Finding rank of a matrix by reducing to Echelon and normal forms
4. Finding the inverse of a non-singular square matrix using row/ column transformations (Gauss- Jordan method)
5. Consistency of system of linear equations (homogeneous and non- homogeneous) using the rank of a matrix
6. Solving m x n and n x n linear system of equations by Gauss elimination.
7. Cayley-Hamilton Theorem (without proof) – Verification. Finding inverse of a matrix and powers of a matrix by Cayley-Hamilton theorem, Linear dependence and Independence of Vectors.
8. Eigen values and eigen vectors of a matrix. Properties of eigen values and eigen vectors of real and complex matrices. Finding linearly independent eigen vectors of a matrix when the eigen values of the matrix are repeated.
9. Diagonalization of matrix -Quadratic forms up to three variables.
10. Rank – Positive definite, negative definite, semi definite, index, signature of quadratic forms
11. Reduction of a quadratic form to canonical form, Nature of quadratic forms
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