: Linear systems and Gaussian elimination. Matrices and matrix operations. Determinants and their properties; invertible matrices. Euclidean and general vector spaces. Linear independence, subspaces, bases, and dimension. Linear transformations in Euclidean and in general vector spaces. Matrix of a transformation relative to fixed bases. Eigenvalues and eigenvectors; matrix diagonalization, and other applications. Inner product spaces, orthogonality; the Gram-Schmidt process. Quadratic forms and symmetric matrices; orthogonal and unitary matrices; applications. Offered each term. Prerequisites: MATH 2216 and MATH 2225 with a grade of C or better, or MATH 3325 with a grade of C or better. Corequisites: None. Restrictions: None. Attributes: Q1 - Quant Reasoning Intensive. .