Linear Algebra for Engineering

Objectives

1- To operate with matrices 2- To calculate the determinant of a matrix and the inverse matrix of an invertible matrix 3- To solve systems of linear equations 4- To determine a basis and the dimension of a vector subspace of 5- To calculate eigenvalues and eigenvectors of a matrix 6-  To identify a linear mapping and its matrix representation

Program

1- Matrices: operations with matrices; invertible matrices; row echelon form; rank of a matrix. 2- Systems of linear equations: classifications; Gauss elimination algorithm;  Gauss-Jordan method for calculating the inverse matrix of an invertible matrix. Crammer systems. 3- Determinants: properties; adjoint matrix of a matrix; adjoint matrix method for calculating the inverse matrix of an invertible matrix. 4- Vector spaces IR^n: 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. 5- Eigenvalues and eigenvectors of a matrix: definition and determination; diagonalisation. 6- Linear mappings from IR^n to IR^m: 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.

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