Self-learning Tutorials
Matrix Algebra
Introduction : Matrix Algebra Refresher
- Outline of the videos
- Prerequisite and notations : vectors
- Prerequisite and notations : matrices
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1. Rank of a Matrix
- The matrix as a set of vectors
- Linear independence
- Linear dependence
- Rank of a matrix: definition and properties
- Exercise 1
- Exercise 2
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2. Trace of a Square Matrix
- Definition
- Properties of the trace
- Exercise 3
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3. Determinant
- Determinant of a square matrix, minor, cofactor
- Determinant of a 3x3 matrix : Sarrus rule
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4. Inverse of a Matrix, Idempotent Matrix
- Inverse of a square matrix: definition
- Non-singular matrix
- Idempotent matrix
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5. Characteristic Roots and Vectors
- Eigenvalues and vectors
- Characteristic equation
- Solved example
- Exercise 4
- Fundamental theorem of algebra
- Eigenvalues and eigenvectors of symmetric matrices
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6. Diagonalization and Spectral Decomposition
- Compact representations
- Diagonalization
- Spectral decomposition
- Example of spectral decomposition
- Exercise 5
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7. Eigenvalues, Trace, Determinant and Rank
- Eigenvalues and trace
- Eigenvalues and determinant
- Eigenvalues and rank