Matrices
A matrix is a rectangular array of numbers arranged in rows and columns. It is usually denoted by uppercase letters, such as A, B, C.
The matrix A here has 3 rows and 3 columns, so it is called a 3×3 matrix.
Matrix Operations
- Addition: two matrices can be added if they are the same size.
- Subtraction: similarly, subtract the values element-wise.
- Scalar multiplication: multiply every element by the scalar.
- Matrix multiplication: not element-wise, but row-column multiplication.
Determinant
The determinant is a number assigned to a square matrix that plays an important role in algebraic calculations. It is particularly useful for inverse matrices and solving systems of linear equations.
Inverse Matrix
The inverse of matrix A, A^{-1}, is a matrix such that A·A^{-1} = I, where I is the identity matrix. Inverse exists only for square and non-singular (determinant ≠ 0) matrices.
Applications
- Solving systems of linear equations.
- In machine learning and neural network computations.
- Computer graphics (transformations, rotations).
- Cryptography and encryption algorithms.
Practice Exercise
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