### 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.