MATH 130--Linear Algebra
David Joyce · Clark Digital Commons (Clark University) · 2015
Course description.Math 130 is a requirement for mathematics and physics majors, and it's highly recommended for majors in other sciences especially including computer-science majors.Topics include systems of linear equations and their solutions, matrices and matrix algebra, inverse matrices; determinants and permutations; real n-dimensional vector spaces, abstract vector spaces and their axioms, linear transformations; inner products (dot products), orthogonality, cross products, and their geometric applications; subspaces, linear independence, bases for vector spaces, dimension, matrix rank; eigenvectors, eigenvalues, matrix diagonalisation.Some applications of linear algebra will be discussed, such as computer graphics, Kirchoff's laws, linear regression (least squares), Fourier series, or differential equations.Prerequisites.The prerequisite for the course is one year of college calculus, others by permission only. Inner products and orthogonalityInner products.Norm and inner products in Cn and abstract inner product spaces.Cauchy's inequality.Orthogonality.Orthogonal matrices.Gram-Schmidt orthonormalisation process Complex matrices and vector spaces Complex numbers.Dave's Short Course on Complex Numbers.Complex vector spaces.Complex matrices.Complex inner product spaces.Hermitian conjugates.