GTU II SEM Maths II Syllabus

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).

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