Linear Algebra and Analytic Geometry MAT1204

Course content:

Linear endomorphisms: eigenvectors and eigenvalues, Jordan form. Dual space and dual basis,refexivity. Bilinear forms, quadratic forms, Lagrange mathod, rela quadratic forms, Jacobi and Sylvester methods, Euclidean spaces, orthogonality, orthogonal decomposition, orthogonalisation Gram-Schmidt algorithm, Determinant as a measure of volume, Gramian determinant. Vector product,Affine spaces, Straight line, plane, affine independence. Algebraic curves and quadric surfaces. Analytical geometry in a 3-dimensional Euclidean space.

Learning outcomes: The students will acquire a basic knowledge of vector and affine spaces. They will learn how to formulate mathematical problems in terms of linear algebra.