Matrix (mathematics)
From Reboil
A Matrix is a rectangular array of numbers arranged in rows and columns.
Stats
Terminology
- column vector
- Cramer's Rule
- determinant
- inversion
- A type of matrix operation such that matrix A multiplied by its inverse A-1 equals an identity matrix.
- matrix
- row vector
- vector
Size
An m by n matrix has m rows and n columns.
A row vector is a a 1 by n matrix.
A column vector is a m by 1 matrix.
Basic Operations
Addition, scalar multiplication, subtraction
Matrix multiplication
Row operations
Submatrix
Linear equations
Linear transformations
Square matrix
Square matrix types
Diagonal matrix
Triangle matrix
Identity matrix
Square matrix operations
Determinant
The determinant can be calculated by multiplying the main diagonal of an upper triangle matrix.
Upper triangle technique
- Givens:
- Adding a multiple of any row to another row, or a multiple of any column to another column does not change the determinant.
- Interchanging two rows or two columns affects the determinant by multiplying it by −1.
- Therefore:
- Using these operations, any matrix can be transformed to a lower (or upper) triangular matrix, and for such matrices, the determinant equals the product of the entries on the main diagonal.
Eigenvalues and eigenvectors
History
Baltakatei history
See also
External links
References
Footnotes
