MA1L302
Undergraduate (ITEP)
· Generally offered: Autumn
Linear Algebra
L 3 T 1 P 0 Credits 4 Hours 4
Unit I: System of Linear Equations, Matrices and elementary row operations, Row reduced echelon form of matrices, Rank of matrices, Vector spaces, subspaces, bases and dimension, column and row spaces.
Unit II: Direct sum of vector space, quotient spaces, Linear Transformation and matrix representation of linear transformation, Rank-Nullity theorem, Dual spaces, transpose and determinants.
Unit III: Eigenvalues and eigenvectors, characteristic polynomials, minimal polynomials, Cayley-Hamilton Theorem and Diagonalization.
Unit IV: Inner product spaces, Gram-Schmidt orthonormalization, orthogonal projections, linear functionals and adjoints, Hermitian, self-adjoint, unitary and normal operators.
Full syllabus document →
Unit II: Direct sum of vector space, quotient spaces, Linear Transformation and matrix representation of linear transformation, Rank-Nullity theorem, Dual spaces, transpose and determinants.
Unit III: Eigenvalues and eigenvectors, characteristic polynomials, minimal polynomials, Cayley-Hamilton Theorem and Diagonalization.
Unit IV: Inner product spaces, Gram-Schmidt orthonormalization, orthogonal projections, linear functionals and adjoints, Hermitian, self-adjoint, unitary and normal operators.
4 questions tagged to this course
4
Votes
Is a matrix populated randomly by 0/1 invertible?
Suppose each entry of a $2\times 2$ matrix is populated with $0$ or $1$ independently with probability $1/2$. What is the probability that this matrix invertible? What will be the …
0
Votes
Rate of convergence of Jacobi and Gauss-Seidel Algorithms
I am aware of the two cases: a) 2X2 matrices b) Stein-Rosenberg case (where a_ii>0, a_ij
0
Votes
Rank–nullity for infinite-dimensional spaces; where does it break?
The finite-dimensional proof leans on a basis argument. What's the right replacement when $V$ is not finite-dimensional?