## What is meant by matrix calculus?

The term "matrix calculations" refers to mathematical operations applied to matrices. Matrices are rectangular arrays of numbers, symbols, or expressions arranged in rows and columns. Matrix calculations are a fundamental part of linear algebra and are used in many fields such as engineering, physics, computer science, and economics.

Typical software functions in the area of "matrix calculations":

- Matrix Creation: Definition and creation of matrices of various sizes and dimensions.
- Basic Operations: Performing basic operations such as addition, subtraction, and multiplication of matrices.
- Transposition: Calculating the transpose of a matrix, where rows and columns are swapped.
- Determinant Calculation: Computing the determinant of a matrix, an important value in linear algebra.
- Inversion: Computing the inverse of a matrix, if it exists.
- Eigenvalue and Eigenvector Calculation: Determining eigenvalues and eigenvectors of a matrix, which are significant in many applications like physics and statistics.
- Diagonalization: Converting a matrix into a diagonal form to simplify calculations.
- Solution Methods: Implementing algorithms to solve linear systems of equations represented in matrix form.
- Visualization: Graphical representation of matrices and their transformations.
- Saving and Loading: Storing matrices and their calculation results and loading this data from files.

Examples of "matrix calculations":

- Calculating the productivity of a company by analyzing input-output matrices.
- Solving network systems in electronics using admittance or impedance matrices.
- Determining transition probabilities in Markov chains.
- Processing image data in computer vision by applying convolution operations on matrices.
- Modeling and simulating physical systems using state equations in control engineering.
- Analyzing financial data through covariance and correlation matrices.