Discover the Systems of Linear Equations
Around the Row Echelon Form of a System
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Discover the Row Echelon form (3:30)
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Back Substitution in Python for Systems in Row Echelon Form (10:12)
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Gaussian Elimination and Back Substitution (10:15)
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Gaussian Elimination and Back Substitution in Python (11:44)
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Gauss Jordan Elimination (5:58)
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Gauss Jordan Elimination in Python (5:05)
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Around the Row Echelon Form of a System (pdf)
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Section 3 Test
Pivoting for Gaussian and Gauss Jordan Elimination
The Case of Singular Matrices
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Examples of Singular Linear Systems with an Infinity of Solutions (15:17)
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Examples of Singular Linear Systems with no Solution (5:53)
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Analyse Singular Systems with Gaussian Elimination with Pivoting (17:03)
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Solve singular systems with Gauss Jordan Elimination with Pivoting (25:46)
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The Case of Singular Matrices (pdf)
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Section 5 Test
The Case of Rectangular Matrices
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Examples of Underdetermined Systems (4:54)
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Analyse Underdetermined Systems with Gaussian Elimination with Pivoting (10:21)
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Solve Underdetermined Systems with Gauss Jordan Elimination with Pivoting (17:35)
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Examples of Overdetermined Systems (23:45)
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Least Square Optimization in Python (24:30)
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The Case of Rectangular Matrices (pdf)
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Section 6 Test
The Homogeneous Systems
Matrices, Line Vectors and Column Vectors
Operations on Matrices and Line or Column Vectors
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Transpose Matrices, Line and Column Vectors (14:38)
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Add and Subtract Matrices and Column Vectors (21:30)
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Multiply and Divide Matrices and Line or Column Vectors by Scalars (26:03)
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Properties of Matrices and Vectors Addtion and Scalar Multiplication (29:46)
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Multiply Matrices, Line Vectors and Column Vectors Together (18:10)
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Matrices and Vectors Multiplication Properties (20:57)
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Operations on Matrices and Line or Column Vectors (pdf)
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Section 9 Test
Invertibility and Inversion of Square Matrices
The Elementary Matrices
The Determinant of a Matrix - Recursive Definition
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Discover the Determinant of a Matrix with Python (11:32)
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Definition of the Determinant of a 2x2 Matrix (2:14)
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Definition of the Determinant of a 3x3 Matrix (6:05)
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Definition of the Determinant of Any Square Matrix (2:27)
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Python Implementation of the Definition of a Determinant (10:29)
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Expansion in Any Row or Column of a Determinant (11:16)
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The Determinant of a Matrix - Recursive Definition (pdf)
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Section 12 Test
Properties of the Determinants
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Linearity of the Determinant in its Lines and Columns (20:10)
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Elementary Row Operations and Determinant (4:06)
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Some Conditions that Yield a Zero Determinant (13:01)
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Determinant with Gaussian Elimination with Pivoting (9:59)
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The Determinant of a Matrix Product (6:43)
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Properties of the Determinants (pdf)
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Section 13 Test
The LU-Factorization of a Matrix
Final Assessment
Conclusion
