# GTU II SEM Maths II Syllabus

Gujarat Technological University

Semester II

Maths II

Vectors in Rn, notion of linear independence and dependence, linear

span of a set of vectors, vector subspaces of Rn, basis of a vector

subspace.

• Systems of linear equations, matrices and Gauss elimination, row space,

null space, and column space, rank of a matrix.

• Determinants and rank of a matrix in terms of determinants.

• Abstract vector spaces, linear transformations, matrix of a linear trans-

formation, change of basis and similarity, rank-nullity theorem.

• Inner product spaces, Gram-Schmidt process, orthonormal bases, pro-

jections and least squares approximation.

• Eigenvalues and eigenvectors, characteristic polynomials, eigenvalues

of special matrices ( orthogonal, unitary, hermitian, symmetric, skew-

symmetric, normal). algebraic and geometric multiplicity, diagonaliza-

tion by similarity transformations, spectral theorem for real symmetric

matrices, application to quadratic forms.

Texts/References

1. H. Anton, Elementary linear algebra with applications (8th Edition),

John Wiley (1995).

2. G. Strang, Linear algebra and its applications (4th Edition), Thom-

son(2006).

3. S. Kumaresan, Linear algebra – A Geometric approach, Prentice Hall

of India (2000).

4. E. Kreyszig, Advanced engineering mathematics (8th Edition), John

Wiley (1999).