MA2031 Linear Algebra for Engineers
Real and Complex Vector Spaces, Subspaces, Span, Linear Independence, Dimension.
Linear Transformations, Rank and Nullity, Matrix Representation, Change of Bases, Solvability of linear systems.
Inner Product Spaces:
Inner products, angle, Orthogonal and orthonormal sets, Gram-Schmidt orthogonalization, Orthogonal and orthonormal basis, Orthogonal Complement, QR-factorization, Best approximation and least squares, Riesz representation and adjoint.
Eigen Pairs of Linear Transformations:
Eigenvalues and Eigenvectors, spectral mapping theorem, characteristic polynomial, Cayley-Hamilton Theorem.
Block-diagonalization, Schur triangularization, Diagonalization Theorem, Generalized eigenvectors, Jordan form, Singular value decomposition, Polar decomposition.
1. S. Lang, Linear Algebra, 3rd edition, Springer, 2004.
2. D W Lewis, Matrix Theory, World Scientific, 1991.
1. K Janich, Linear Algebra, Springer, 1994.
2. B Koleman and D Hill, Elementary Linear Algebra, 9th edition, Pearson, 2007.
3. H Anton, C Rorres, Elementary Linear Algebra: Applications, 11th edition, Wiley, 2013.