1. Rank
2. Subspicies,a partial case - blue arrow Properties - red arrow Descriptive concept - green Form - purple Component - orange Corollary - grey
3. Determinant
3.1. non-zero
3.2. zero
4. Minor
4.1. Cofactor
4.1.1. Adjugate matrix
5. Vector space
5.1. subspace
5.1.1. null space
5.1.2. column space
5.1.3. row space
5.1.4. left nullspace
5.2. dimension
5.2.1. finite-dimension
5.2.2. infinite-dimension
6. Linear Combinations
6.1. linearly independent
6.2. linearly dependent
7. Span
8. Composition
9. Distance
9.1. shortest
10. Norm
10.1. Euclidean
10.2. Manhattan
10.3. maximum-coordinate
11. Theorems for orthogonality
11.1. Least square solution
11.2. Pythagorean theorem
11.3. Triangle inequality
11.4. Cauchy–Bunyakovsky–Schwarz inequality
12. Regression
12.1. Linear
12.2. Polynomial
12.3. Multiple
13. Projection
13.1. line
13.2. subspace
14. Linear Systems
14.1. Ax=b, b - any number
14.1.1. Homogeneous
14.1.2. Non-homogeneous
15. Solutions
15.1. Elimination
15.1.1. Gaussian- and Jordan elimination
15.2. Substitution
15.3. Graphing
15.4. Conjugate gradient method
16. Matrices
16.1. Special
16.1.1. zero
16.1.2. square
16.1.3. diagonal
16.1.4. identity
16.1.5. elementary
16.1.6. rectangular
16.1.7. similar
16.1.8. unitary
16.1.9. idempotent
16.1.10. symmetric
16.1.10.1. Hermitan
16.1.11. anti-symmetric
16.1.11.1. Skew - Hermitan
16.2. Transformed
16.2.1. REF
16.2.1.1. RREF
16.2.2. Triangular
16.2.2.1. upper triangular
16.2.2.2. lower triangular
17. Uniqness
18. Existence
19. Consistence
20. Variables
20.1. Free var.
20.2. Pivot
21. Vectors
22. Invertibility
22.1. Invertible matrix
22.1.1. Right- and left-invertibility
22.1.2. Invertibility of a product
22.2. Non-invertible matrix
22.3. Pseudo-invertible matrix
23. Operations
23.1. basic
23.1.1. elementary row
23.2. multiplication
23.2.1. vector-vector
23.2.2. matrix-matrix
23.2.3. vector-matrix
24. Basis
25. Coordinates with respect to basis
26. Coordinate Mapping
26.1. linear
26.2. isomorphic
27. Transformations
27.1. Change of basis
28. Orthogonality
28.1. Orthogonal
28.2. Orthonormal
29. Decomposition
29.1. Orthogonal
29.2. LU
29.3. Gram–Schmidt
29.4. QR
29.4.1. reduced
29.4.2. full
29.4.3. Householder’s reflections