Knowledge of Mathematics

Detailed proofs will be provided as clear as possible

Knowledge of Mathematics

Detailed proofs will be provided as clear as possible

Linear Algebra

Arithmetic Operations of Matrices

Matrices
Elementary Row and Column Operations of Matrices
System of Linear Equations

Vector Spaces

Concepts and Definitions
Subspaces
Independence
Bases and Dimensions
Finite-Dimensional Vector Spaces
Maximal Set of Linearly Independent Vectors
Coordinates
Direct Sums and Direct Product

Linear Mappings

Matrices and Linear Mappings

Dual space

Eigenvalues and Eigenvectors

Decomposition of Vector Spaces

The Jordan Normal Form

The Rational Normal Form

Inner Product Spaces

Bilinear Mappings