Mathematics-II Syllabus
Linear algebra — vector spaces, matrices and Gauss elimination, linear transformations, inner product spaces and eigenvalues.
Syllabus — 6 Units
- 1
Vectors in Rⁿ
Linear independence and dependence, linear span, vector subspaces of Rⁿ, basis of a vector subspace.
- 2
Systems of Linear Equations
Matrices and Gauss elimination, row space, null space, column space, rank of a matrix.
- 3
Determinants
Determinants and rank of a matrix in terms of determinants.
- 4
Linear Transformations
Abstract vector spaces, matrix of a linear transformation, change of basis and similarity, rank-nullity theorem.
- 5
Inner Product Spaces
Gram-Schmidt process, orthonormal bases, projections and least squares approximation.
- 6
Eigenvalues & Eigenvectors
Characteristic polynomials, special matrices, algebraic & geometric multiplicity, diagonalization, spectral theorem, quadratic forms.