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Mathematical Methods-II

  •  Units 4
  •  Lessons 23
  •  No. of Downloads 389
  •  Course Type Post Graduate
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Syllabus

Linear Algebra: Group, ring, field and vector spaces, Sub-spaces, basis, Gram Schmidt’s orthogonalization, Galois field - Fermat’s theorem and primitive elements. Linear transformations. Graph theory: Concepts and applications.

Group

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Subgroup

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Cayle's Theorem

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Ideals

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Vector Space

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Gram Schmidt Orthogonalization

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Galois Theory

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Linear Transformation

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Graphs

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Syllabus

Matrix Algebra: Basic terminology, linear independence and dependence of vectors. Row and column spaces, Echelon form. Determinants, rank and inverse of matrices. Special matrices – idempotent, symmetric, orthogonal. Eigen values and eigen vectors. Spectral decomposition of matrices.

Matrix Algebra

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Linear Independence and Dependence of Vectors

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Row and Column Spaces and Echelon Form

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Determinants

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Rank and Inverse of Matrix

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Eigen Values, Eigen Vectors and Spectral Decomposition of Matrix

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Syllabus

Unitary, Similar, Hadamard, Circulant, Helmert’s matrices. Kronecker and Hadamard product of matrices, Kronecker sum of matrices. Sub-matrices and partitioned matrices, Permutation matrices, full rank factorization, Grammian root of a symmetric matrix. Solutions of linear equations, Equations having many solutions.

Special Matrices

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Operations on Matrices and Grammian Root

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Full Rank Factorization

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Solutions of System of Linear Equations

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Syllabus

Generalized inverses, Moore-Penrose inverse, Applications of g-inverse. Spectral decomposition of matrices, Inverse and Generalized inverse of partitioned matrices, Differentiation and integration of matrices, Quadratic forms.

Generalized Inverses

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Spectral decomposition of matrices, Inverse and Generalized inverse of partitioned matrices

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Differentiation and Integration of Matrices

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Quadratic forms

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