Objectives
- To operate with matrices
- To calculate the determinant of a matrix and the inverse matrix of an invertible matrix
- To solve systems of linear equations
- To determine a basis and the dimension of a vector subspace of
- To calculate eigenvalues and eigenvectors of a matrix
6. To identify a linear mapping and its matrix representation
Program
- Matrices: operations with matrices; invertible matrices; row echelon form; rank of a matrix.
- Systems of linear equations: classifications; Gauss elimination algorithm; Gauss-Jordan method for calculating the inverse matrix of an invertible matrix. Crammer systems.
- Determinants: properties; adjoint matrix of a matrix; adjoint matrix method for calculating the inverse matrix of an invertible matrix.
- Vector spaces ℝⁿ: linear independence; vector subspaces; generators of a vector subspace; basis and dimension of a vector subspace. Representation of a vector subspace by a system of linear equations.
- Eigenvalues and eigenvectors of a matrix: definition and determination; diagonalisation.
- Linear mappings from ℝⁿ to ℝᵐ: matrix representation; sum and composition; kernel and image; nullity and rank of a matrix.
Bibliography
- Santana, Ana Paula; Queiró, João Filipe. (2010) Introdução à Álgebra Linear; Gradiva, Trajectos Ciência
- Lang, Serge. (2004) Introduction to Linear Algebra 3rd edition. Springer, Undergraduate Texts in Mathematics.
- Strang, Gilbert. (2016) Introduction to Linear Algebra - 5th edition, Wellesly Cambridge Press
- Lay, David; Lay, Steven; McDonald, Judith. (2016) Linear Algebra and Its applications - 5th edition.
Pearson Education,Inc.