Linear Algebra I / Introduction to Linear Algebra
Vector spaces, systems of linear equations, matrices, Gaussian elimination, symmetric matrices, the adjoint of a matrix, the transpose of a matrix, determinant of a matrix, the inverse of a matrix. Cramer's rule. Inner product spaces, eigenvalues and eigenvectors. Systems of linear inequalities and systems of differential equations. Orthogonal projections and orthogonality, orthonormality and orthonormal basis as well as standard basis. Classical theorems of vector analysis [Green, Gauss and Stokes].
