2:08:14
**UNIT 2**

Eigen values-Eigen Vectors and Quadratic forms: Eigen Values and Eigen vectors, Properties, Problems on Eigen Values and Eigen vectors, Problems on Eigen Values and Eigen vectors Part 1, Cayley-Hamilton theorem, Problems on Cayley-Hamilton theorem, Problem Inverse and Powers of matrix by using Cayley-Hamilton theorem, Diagonalization, Problem on Diagonalization, Quadratic forms, Reduction of a Quadratic form to Canonical form, Problems on Reduction of a Quadratic form to Canonical form Part 1, Problems on Reduction of a Quadratic form to Canonical form Part 2, Problems on Reduction of a Quadratic form to Canonical form Part 3, Problems on Reduction of a Quadratic form to Canonical form Part 4, Rank , Positive,Negative forms Quadratic form, Semi-definite and indefinite forms of Quadratic form, Index and Signature of a quadratic form, Applications: Free Vibration of a two-mass system