Linear Algebra

[Linear Algebra] 11. LU decomposition

Definition of LU decomposition, Gauss elimination

[Linear Algebra] 10. Eigenvalues, Eigenvectors, and Decomposition

Eigenvalues, Eigenvectors, and…

[Linear Algebra] 9. Properties of orthogonal matrices

1. Definition of an orthogonal matrix

[Linear Algebra] 8. Linear Independence and Non-singular Matrix

1. Linear Independence

If a vector 𝐯, in a set of vectors 𝐒 in vector space 𝐕, can be expressed as a linear combination of other vectors it is called linear dependent. If that…

[Linear Algebra] 7. Kernel, Image and Rank-Nullity Theorem

Kernel, Image, Rank, and the dimension…

[Linear Algebra] 6. Gauss-Jordan Elimination

Elementary Matrix Operations, Echelon Form, Gauss-Jordan…

[Linear Algebra] 5. Determinant

Definition and properties of the determinant

[Linear Algebra] 4. Matrix Types

Square, Triangle, Diagonal, Identity, Orthogonal Matrices.

[Linear Algebra] 3. Dot Product

Definition of the Dot product

[Linear Algebra] 2. Basis

Vector Space, linear independence, and Basis