Course Details
Contents
1. Vectors: 2D and 3D, scalar and vector product, norm.
2. Matrices: Linear independence, rank, matrix equations-row reduction, inverse, least squares, pseudo-inverse, applications in circuit analysis.
3. Spectral decomposition - Eigenvalues and eigenvectors, characteristic polynomial and its properties, Cayley-Hamilton Theorem, SVD, Quadratic forms
4. Matrix decompositions - LU and Cholesky decomposition, QR and Schur decomposition,
5. Special matrices: Toeplitz, Circulant, Fourier etc. and their applications in signal processing.
6. Solutions to systems of ordinary differential equations, matrix exponent
References
1. G V V Sharma, Matrices in Geometry.
2. David Lay, Linear Algebra and Its Applications
3. G. Strang. Introduction to Linear Algebra, Wellesley Cambridge Press.
4. R. A. Horn and C. R. Johnson Matrix Analysis, Cambridge University Press.
5. S. Boyd and L. Vandenberghe, Introduction to Applied Linear Algebra, Vectors, Matrices, and Least Squares, Cambridge University Press.