Description

Theory
1

Theory/Practice
2

Instructors

Ana Moura

Contents

1. Matrix Calculus (3weeks,20%)
Definition and representation. Equality of matrices. Transpose of a matrix and symmetric matrix.
Matrix operations. Properties.
Elementary row operations. Matrices equivalency. Condensation of a matrix.
Rank of a matrix; Gauss Elimination?s Method (GEM).
Inverse of a matrix; computation by GEM.
 

2. Determinants (3weeks,20%)
Definition. Evaluating 2nd and 3rd order determinants.
Laplace's Theorem. Evaluating determinants of any finite order.
Properties.
Computation of the inverse of a matrix using the adjoint matrix.
 

3. Systems of linear equations (3weeks,20%)
Matrix notation.
The Cramer's Rule.
Discussion and resolution by GEM.
 

4. Real vector spaces (3weeks,20%)
Definition and properties.
Subspaces.
Linear combinations. Generated subspace. Linear dependence.
Basis and dimension.
 

5. Linear transformations (3weeks,20%)
Definition and properties.
Matrix of a transformation.
Kernel and image.
Eigenvalues and eigenvectors.

Learning Outcomes

OB1: Perform fundamental matrix operations, determine matrix inverses, and solve matrix equations.

OB2: Calculate determinants and apply determinant properties to solve mathematical problems.

OB3: Use matrix and determinant methods to solve and analyse systems of linear equations.

OB4: Identify and operate with real vector spaces, vectors, and bases.

OB5: Analyse linear transformations, determine associated matrices, and calculate eigenvalues and eigenvectors.