MA2031 Linear Algebra for Engineers

Course Details

Vector Spaces:
Real and Complex Vector Spaces, Subspaces, Span, Linear Independence, Dimension.
Linear Transformations:
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.
Matrix Representations:
Block-diagonalization, Schur triangularization, Diagonalization Theorem, Generalized eigenvectors, Jordan form, Singular value decomposition, Polar decomposition.

Course References:

Text:
1. S. Lang, Linear Algebra, 3rd edition, Springer, 2004.
2. D W Lewis, Matrix Theory, World Scientific, 1991.

REFERENCES:
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.