Introduction to the main concepts of linear algebra on which most data science tools are based.

The connection between this domain and data science will be detailed in several examples (linear regression, NLP, PCA).

The emphasis will be placed on vectors, matrices, the determinant and its byproducts (inverse, eigenvalues/eigenvectors of a square matrix and diagonalization).

The Numpy library will be introduced to implement these concepts in Python.

Session 1 :
- Connection Between Linear Algebra And Data Science
- Linear System Of Equation And Linear Transformations: Intuition Of Vectors And Matrices
- Vectors And Matrices To Represent Information In Data Science: TheLinear Regression Example - Matrix/Matrix, Vector/Vector Sum And Matrix/Vector, Scalar/Vector, Scalar/Matrix Products - Dot Product And Norm (Example Of Their Use With Embeddings In Nip)

Session 2 :
- Linear Combination, Linear Independence, Span
- Vector Space
- Basis And Dimension

Session 3 :
- The Determinant Of A Matrix And Its Properties
- Inverse Of A Square Matrix
- Eigenvalues And Eigenvectors Of A Square Matrix

Session 4:
- Change Of Basis
- Diagonalization Of A Matrix
- Orthogonal And Symmetric Matrices
- Use of Linear Algebra For Dimensionality Reduction : The Example Of ThePca
- Quick Introduction To Tensors