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Linear Algebra in the Euclidean Plane

Preliminaries

Get an Editable Window for a Figure in Python (9:09)
Introduction (5:30)
Linear Equations of One Variable (4:52)

Example of System of 2 Equations of 2 Variables

Let's solve a Puzzle (2:29)
Solve the System obtained (4:41)
The Matrix View (6:09)
The Matrices and Vectors in Python (12:57)
Around the Solution of a Puzzle (pdf)
Section 2 Test

The Systems of 2 Linear Equations in 2 Variables

Solve any 2x2 Linear System (8:04)
The Matrix View (general case) (6:50)
The Matrix Proof of the Matrix Equation Solution (20:07)
The case of a Zero Determinant (10:03)
Solve 2x2 Linear Systems (pdf)
Section 3 Test

The Vectors in the Euclidean Plane

Let's Draw some Vectors (9:31)
The Generic Vectors in the Plane (9:08)
Add and Subtract Two Vectors (15:27)
Multiply or Divide a Vector by a Scalar (16:05)
Structure of Vector Space (18:07)
The Canonical Vector Plane P (pdf)
Section 4 Test

The Dot Product and the Norm of Vectors

The Dot Product of Two Vectors (9:33)
The Orthogonality of Two Vectors (3:12)
The Norm of a Vector (10:59)
The Norm of a Vector as its Length (12:12)
The Dot Product and the Norm in the Euclidean Plane (pdf)
Section 5 Test

Angles in Radian and Trigonometric Functions

Oriented Angle of a Unit Vector with the x Axis (4:37)
Trigonometry in the Unit Circle (10:22)
The Trigonometric Functions in the Real Set (3:59)
Angle of any Non Zero Vector with the x Axis (8:56)
Angles between any Two Non-Zero Vectors (6:14)
Angles in Radians and Trigonometric Functions (pdf)
Section 6 Test

The Polar Coordinates and the Rotations

Discover the Polar Coordinates (5:04)
Particular Configurations of Polar Angles (3:30)
Convert Cartesian Coordinates into Polar Coordinates (8:10)
Rotation of a Vector in Polar Coordinates (4:32)
The Polar Coordinates and the Rotations (pdf)
Section 7 Test

The Complex Numbers as Vectors

Discover the Complex Numbers (14:14)
The Complex Numbers in Python (5:20)
Add, Subtract, Multiply and divide Complex Numbers (7:21)
The Module and Argument of a Complex Numbers (5:07)
The Complex Exponential in Python (4:34)
Rotations as Multiplications by Complex Numbers (3:31)
The complex Numbers as Vectors (pdf)
Section 8 Test

The Linear Mappings and their Matrices

The Linear Mappings, Definition and Examples (4:26)
The Matrix of a Linear Mapping (5:03)
Addition, Subtraction and Scalar Multiplication of Linear Mappings (14:37)
Composition of Linear Mappings (13:03)
Kernel, Range and Rank of a linear mapping (11:50)
The Linear Mappings and their Matrices (pdf)
Section 9 Test

Bases and Change of Basis

Definiton of a Basis in P (20:55)
Change of Basis and Transition Matrix (20:04)
Change of Basis for the Matrix of a Linear Mapping (9:35)
Direct and Reverse Orthonormal Bases (17:26)
Bases in the Plane and Change of Basis (pdf)
Section 10 test

Symmetric, Skew Symmetric and Unit Matrices

The Transpose of a Matrix (16:29)
Symmetric and Skew Symmetric Matrices (8:16)
Transpose of a Column Vector (12:41)
Unit Matrices (11:59)
Symmetric, Skew Symmetric and Unit Matrices (pdf)
Section 11 test

Eigenvalues and Eigenvectors

Examples of Eigenvalues and Eigenvectors (3:00)
Eigenvalues and Eigenvectors of a Linear Mapping (7:40)
Homogenous Linear Systems (4:21)
Calculation of the Eigenvalues of a Linear Mapping (8:56)
Eigenvectors and Diagonalisation (9:48)
Eigenvalues and Eigenvectors (pdf)
Section 12 test

Diagonalisation in the Field of Complex Numbers

The Field of Complex Numbers (21:54)
Conjugate Complex Numbers (14:13)
Resolution of quadratic equations in C (13:34)
Matrices and Column Vectors with Complex Elements (18:06)
2x2 Linear Systems in C (4:41)
Diagonalisation in C of Real Matrices (15:10)
Diagonalisation in the Field of Complex Numbers (pdf)
Section 13 test

Final Assessment

Subject of the Assesment

Conclusion

Conclusion (4:33)

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Introduction

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