Linear Algebra and Analytical Geometry

All lectures: All lectures at the Academy of Intelligence on the discipline: linear algebra and analytical geometry. These fascinating lectures provide us with the opportunity to explore the deep principles and phenomena underlying our knowledge and our desire to understand the world.
1. Second-Order Curves and Surfaces
2. Analytic Geometry
3. Vectors in Linear Algebra and Programming
4. Quaternion History
5. 1. Elements of linear algebra 1. The determinants of the second and third orders
6. 1. Elements of linear algebra 2. Kramer’s method for solving systems of algebraic equations
7. 2.1. Concept of geometric vector
8. 2.2. Vector module
9. 2.3. Basis of vector and coplanar vectors
10. 2.4. The decomposition of the vector basis
11. 2.5. Right three vectors
12. 2.6. Projection of vector onto vector
13. 2.7. Orthonormal basis
14. 2.8. Scalar product of vectors and its properties
15. 2.9. Vector product of vectors and its properties
16. 2.10. Mixed product of vectors and its properties
17. 3.1. Definition of a rectangular Cartesian coordinate system
18. 3.2. Finding the coordinates of a vector given by two points
19. 3.3. Linear vector operations
20. 3.4. The products of vectors in PDK
21. 3.5. The condition for determining the basis
22. 3.6. Polar coordinates
23. Elements of analytical geometry 1.4.1. Direct in space
24. 4.2. Plane in space
25. 4.3. Straight line on a plane
26. 4.4. Second order curves
27. 4.5. Ellipse
28. 4.6. Hyperbola
29. 4.7. Parabola
30. Examples of solving problems to the section Linear algebra and analytic geometry
31. Matrix and Gram determinant
32. LINEAR FORM
33. Spline: Concept and Types
34. The Concept of a Matrix as a Mathematical Object, Operations on Matrices, and Applications
35. Matrix Decomposition: LU Decomposition (LR), Cholesky Decomposition, and Singular Value Decomposition
36. 2.9 Pseudoscalar Product
37. Quaternion
38. Euler Angles (Nutation, Precession, Rotation) and Tait–Bryan Angles (Yaw, Pitch, Roll), Quaternions
39. Spherical Coordinate System (Azimuth and Zenith)
40. Tensor Calculus and Tensors
41. Eigenvector
42. Covariance and Contravariance (Mathematics)
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