Linear Algebra

What you’ll study

Vectors in Rⁿ and Cⁿ: review of geometric vectors in R² and R³ space, inner product, norm and distance in Rⁿ and Cⁿ. Matrices and determinants: notion of a matrix, types of matrices, matrix algebra, the determinant function and its properties, minors and cofactors, expansion and evaluation of determinants, elementary row and column operations, row-reduced echelon matrices, invertible matrices, block matrices. System of linear equations: homogeneous and non-homogeneous systems, and determinants for solving systems. Linear transformations: kernel and image of a linear transformation and their properties, matrix representation, change of basis. Eigenvalues and eigenvectors: diagonalization and applications.