MATE-1106 Linear Algebra I (Honors)

The content of this course is the same as MATE-1105 but in more depth. Vectors in the Euclidean space, scalar product and rule. Matrices and their algebra, linear equation systems. Inverse squared matrices, homogeneous systems, subspaces and bases. Independence and dimension, the range of a matrix. Linear transformations in Euclidean spaces, linear transformations of a plane. Vector spaces, basic concepts in vector spaces, vectors in coordinates. Determinants and linear transformations. Volume areas and cross product, the determinant of a squared matrix, calculation of determinants and Cramer’s rule. Values and vectors, diagonalization and applications. Projections, the Gram-Schmidt orthogonalization process, orthogonal matrices. Projection matrix and the minimum square method. Base change, matrix representations and similarity. Diagonalization of quadratic forms, applications on geometry.