**Linear Algebra**

**Linear algebra is a branch of mathematics concerning linear equations and linear maps, and their representations in vector spaces and through matrices. Linear algebra is central to almost all areas of mathematics.**

**In a course on linear algebra, one may deal with the following topics:**

**Systems of linear equations****Row reductions and echelon forms****Vector and matrix equations****Solution sets of linear systems****Linear independence****Linear transformations and their matrices****Matrix operations, the inverse of a matrix, and characterizations of invertible matrices****Matrix factorization (LU factorization)****Subspaces of****n****-****dimensional real vector spaces****Introduction to determinants and their properties****Cramer's rule and volume, and linear transformations****Null and column spaces****Bases and the dimension of a real vector space****Rank****Change of basis****Eigenvectors, eigenvalues, and eigenspaces****The characteristic equation****Matrix diagonalization****Inner product, length, and orthogonality****Orthogonal sets and projections****The Gram-Schmidt process****The Least square problems and linear regression****Diagonalization of symmetric matrices****Quadratic forms****Constrained optimization****The singular value decomposition (SVD)**

For more details, refer to the following book:

Lay, D. C. (2016). Linear Algebra and its applications 5th edition. Pearson.