Applied Linear Algebra - [2710710]

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Teaching Scheme

Theory
Tutorial Practical Total
3 2 0 5

Examination Scheme

Theory Examination Practical Examination Total
ESE (E) PA (M) ESE Viva (V) PA (I)
70 30 30 20 150

    ESE = End Semester Examination, PA = Progressive Assessment


Semester   
:   
1
Course Type   
:   
Regular
Credit   
:   
4

Syllabus Content

Finite dimensional vector space, subspaces, linear independence, bases and dimension
Algebra of transformations, range and null space of a linear transformation, matrix algebra, simultaneous equations
Sum and intersection of subspaces, direct sum of invariant subspaces, eigen values, characteristic vectors, Cayley-Hamilton theorem, minimal polynomial, Sylvester’s interpolation method, various canonical form. Algebra of polynomial matrices, invariant
Polynomial matrices, invariant polynomials, elementary divisors,Smith canonical form. Innerproduct spaces, Gram Schmidt orthogonalization, linear transformation and their adjoint, self adjoint, unitary and normal transformations, polar decomposition
Some computational methods of linear algebra.

Reference Books

SrTitleAuthorPublicationAmazon Link
1Introduction to Matrices and linear TransformationFinkbeiner D.T.D.B. Taraorewala’s   
2Linear AlgebraHoffman, K and Kunze, R.Prentice Hall of India   
3The Theory of MatricesGantmocher F.R.Cheisea   
4Computational methods in Linear AlgebraGoult, R.J., Hoskin, R.P., Milner, J.A and Pratt,Stanley Thomas Pub. Ltd.

Course Outcome

After learning the course the students should be able to

  •  Understand the vector spaces, transformation
  •  Solve the engineering problems using linear algebra
  •  Use the theorms and canonical forms
  • Use the computational methods for linear algebra