4 Credit Hour Course
Intended For Level 1 Term 2 Students
Prerequisite:
Introduction to vectors, their products, matrices and systems of linear equations; Solving linear equations: Gaussian elimination, inverse and transpose of a matrix, factorization into A = LU; Vector spaces and subspaces: four fundamental subspaces, solving Ax = 0 and Ax = b, independence, basis and dimension, dimensions of the four subspaces; Orthogonality: orthogonality of the four subspaces, projections, least squares, orthonormal bases and Gram-Schmidt; Determinants: properties, formulas, Cramer’s rule, inverses and volumes; Eigenvalues and eigenvectors: eigendecomposition, systems of differential equations, symmetric and positive definite matrices; Singular value decomposition (SVD): bases and matrices in the SVD, geometry of the SVD; Linear transformations: the matrices of linear transformations; Complex vectors and matrices: complex numbers, polar coordinates, Hermitian and unitary matrices; Applications of linear algebra in computer science and engineering.
