Courses
sowiso logo Linear Algebra

Open course Linear Algebra offered by the Teaching and Learning Centre of FNWI.

Authors: André Heck, Jolien Oomens, Marthe Schut

Available languages: 
nlen
Course content
Vectors
The notion of vector and vector space
THEORY
T
1.
Vectors in a plane or space
PRACTICE
P
2.
Vectors in a plane
2
THEORY
T
3.
Algebra with vectors in a plane
PRACTICE
P
4.
Vector algebra
2
THEORY
T
5.
Coordinate system
THEORY
T
6.
Vectors in ℝ2 and ℝ3
PRACTICE
P
7.
Vectors in ℝ2 and ℝ3
8
THEORY
T
8.
The notion of vector space and linear combination of vectors
PRACTICE
P
9.
Linear combination of vectors
4
THEORY
T
10.
The vector space ℝn
Lines and planes
THEORY
T
1.
Vector representation of a line in a plane
PRACTICE
P
2.
Vector representation of a line
7
THEORY
T
3.
Vector representation of a line and plane in ℝ3
PRACTICE
P
4.
Vector representation of a line and plane in space
6
Distance, angle, dot product and cross product
THEORY
T
1.
Length and distance
PRACTICE
P
2.
Length and distance
4
THEORY
T
3.
Dot product, angle and orthogonal projection
PRACTICE
P
4.
Dot product, angle, and orthogonal projection
8
THEORY
T
5.
Normal vector in ℝ2
PRACTICE
P
6.
Normal vector in ℝ2
2
THEORY
T
7.
Normal vector and cross product in ℝ3
PRACTICE
P
8.
Normal vector and cross product in ℝ3
5
THEORY
T
9.
Applications
Vector calculus in MATLAB
THEORY
T
1.
Creation of vectors
THEORY
T
2.
Selection of components, and assignment of values
THEORY
T
3.
Computing with vectors
Vector calculus in Python
THEORY
T
1.
Creation of vectors
THEORY
T
2.
Selection of components, and assignment of values
THEORY
T
3.
Computing with vectors
Vector calculus in R
THEORY
T
1.
Creation of vectors
THEORY
T
2.
Selection of components, and assignment of values
THEORY
T
3.
Computing with vectors
Systems of linear equations
Basic concepts and methods
THEORY
T
1.
The notion of linear equation
PRACTICE
P
2.
The notion of linear equation
4
THEORY
T
3.
Reduction to a basic form
PRACTICE
P
4.
Reduction to a basic form
3
THEORY
T
5.
Solving a linear equation with a single unknown
PRACTICE
P
6.
Solving a linear equation with a single unknown
6
THEORY
T
7.
Solving a linear equation with several unknowns
PRACTICE
P
8.
Solving a linear equation with several unknowns
5
Systems of linear equations
THEORY
T
1.
The notion of a system of linear equations
PRACTICE
P
2.
The notion of a system of linear equations
3
THEORY
T
3.
Homogeneous and nonhomogeneous systems of lineair equations
PRACTICE
P
4.
Homogeneous and nonhomogeneous systems of linear equations
6
THEORY
T
5.
Elementary operations on systems of linear equations
PRACTICE
P
6.
Elementary operations on systems of linear equations
9
System of linear equations and matrices
THEORY
T
1.
From systems of linear equations to matrices
PRACTICE
P
2.
From systems of linear equations to matrices
8
THEORY
T
3.
Equations and matrices
PRACTICE
P
4.
Equations and matrices
9
THEORY
T
5.
Echelon form and reduced row echelon form
PRACTICE
P
6.
Echelon form and reduced echelon form
4
THEORY
T
7.
Row reduction of a matrix to a reduced echelon form
PRACTICE
P
8.
Row reduction of a matrix to a reduced echelon form
3
THEORY
T
9.
Solving systems of linear equations by Gaussian elimination
PRACTICE
P
10.
Solving systems of linear equations by Gaussian elimination
5
THEORY
T
11.
Solvability of systems of linear equations
PRACTICE
P
12.
Solvability of systems of linear equations
3
THEORY
T
13.
Systems with a parameter
PRACTICE
P
14.
Systems with a parameter
3
Solving systems of linear equations in MATLAB
THEORY
T
1.
Solving systems via linsove and solve
Solving systems of linear equations in Python
THEORY
T
1.
Solving systems via linsolve and solve
Solving systems of linear equations in R
THEORY
T
1.
Solving systems via solve and rref
Matrices
Matrices
THEORY
T
1.
The notion of matrix
PRACTICE
P
2.
The notion of matrix
5
THEORY
T
3.
Simple matrix operations
PRACTICE
P
4.
Simple matrix operations
7
THEORY
T
5.
Multiplication of matrices
PRACTICE
P
6.
Multiplication of matrices
10
THEORY
T
7.
The inverse of a matrix
PRACTICE
P
8.
The inverse of a matrix
4
THEORY
T
9.
Determinant of a matrix
THEORY
T
10.
Row and column expansion of a determinant
PRACTICE
P
11.
Determinant of a matrix
5
THEORY
T
12.
Computing determinants
PRACTICE
P
13.
Computing determinants
4
Matrices in MATLAB
THEORY
T
1.
Basic properties and creation of matrices
THEORY
T
2.
Selection of components and assignment of values
THEORY
T
3.
Computing with matrices and vectors
THEORY
T
4.
Row reduction and determinant
Matrices in Python
THEORY
T
1.
Basic properties and creation of matrices
THEORY
T
2.
Selection of components and assignment of values
THEORY
T
3.
Computing with matrices and vectors
THEORY
T
4.
Row reduction and determinant
Matrices in R
THEORY
T
1.
Basic properties and creation of matrices
THEORY
T
2.
Selection of components and assignment of values
THEORY
T
3.
Computing with matrices and vectors
THEORY
T
4.
Row reduction and determinant
Linear mappings
Introduction
THEORY
T
1.
Introduction
Linear mappings
THEORY
T
1.
The concept of linear mapping
PRACTICE
P
2.
The notion of linear mapping
8
THEORY
T
3.
Composition of linear mappings
PRACTICE
P
4.
Composition of linear mappings
2
THEORY
T
5.
The inverse of a linear mapping
THEORY
T
6.
Kernel and image of a matrix mapping
THEORY
T
7.
Criteria for invertibility
PRACTICE
P
8.
Kernel and image of a matrix mapping
4
THEORY
T
9.
Finding the matrix that determines a linear mapping
PRACTICE
P
10.
Finding the matrix that determines a linear mapping
1
Matrices and coordinate transformations
THEORY
T
1.
Introductory example
THEORY
T
2.
Transition to a different coordinate system
PRACTICE
P
3.
Transition to another coordinate system
2
THEORY
T
4.
Similar matrices
PRACTICE
P
5.
Colour and intensity of light
8
Linear mappings in MATLAB
THEORY
T
1.
Kernel and image
THEORY
T
2.
Similarity
Linear mappings in Python
THEORY
T
1.
Kernel and image
THEORY
T
2.
Similarity
Linear mappings in R
THEORY
T
1.
Kernel and image
THEORY
T
2.
Similarity
Eigenvalues and eigenvectors
Eigenvalues and eigenvectors
THEORY
T
1.
The notion of eigenvalue and eigenvector
PRACTICE
P
2.
The notion of eigenvalue and eigenvector
5
THEORY
T
3.
Eigenvalues and eigenvectors of a matrix
PRACTICE
P
4.
Eigenvalues and eigenvectors of a matrix
3
THEORY
T
5.
Computing eigenvectors for a given eigenvalue
PRACTICE
P
6.
Eigenvalues and eigenvectors of a matrix
2
THEORY
T
7.
Computing eigenvalues
PRACTICE
P
8.
Computing eigenvalues
2
THEORY
T
9.
Solving an eigenvalue problem
PRACTICE
P
10.
Solving an eigenvalue problem
2
THEORY
T
11.
Diagonalisability
Eigenvalues and eigenvectors in MATLAB
THEORY
T
1.
Eigenvalues and eigenvectors
Eigenvalues and eigenvectors in Python
THEORY
T
1.
Eigenvalues and eigenvectors
Eigenvalues and eigenvectors in MATLAB
THEORY
T
1.
Eigenvalues and eigenvectors
SVD, pseudoinverse, and PCA
SVD: singular value decomposition
THEORY
T
1.
Singular value decomposition
THEORY
T
2.
Pseudoinverse and the least squares method
THEORY
T
3.
PCA: Principal Component Analysis
SVD, pseudoinverse and PCA in MATLAB
THEORY
T
1.
SVD and digital image compression
THEORY
T
2.
PseudoInverse
THEORY
T
3.
PCA
SVD, pseudoinverse and PCA in Python
THEORY
T
1.
SVD and digital image compression
THEORY
T
2.
PseudoInverse
THEORY
T
3.
PCA
SVD, pseudoinverse and PCA in R
THEORY
T
1.
SVD and digital image compression
THEORY
T
2.
Pseudoinverse
THEORY
T
3.
PCA