Triangular Matrix
A Triangular Matrix is a square matrix whose cells above of below a matrix diagonal or zero cells.
- Context:
- It can range from being a Lower Triangular Matrix to being an Upper Triangular Matrix.
- Example(s):
- [math]\displaystyle{ \begin{bmatrix}1.2 & 0 & 0 \\20 & 55 & 0 \\20 & 55 & 6 \end{bmatrix}. }[/math]
- Counter-Example(s):
- See: Main Diagonal, Diagonal Matrix, Numerical Analysis, Triangular Factorization, Invertible Matrix, Minor (Linear Algebra), Triangular Array.
References
2014
- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Triangular_matrix Retrieved:2014-9-27.
- In the mathematical discipline of linear algebra, a triangular matrix is a special kind of square matrix. A square matrix is called lower triangular if all the entries above the main diagonal are zero. Similarly, a square matrix is called upper triangular if all the entries below the main diagonal are zero. A triangular matrix is one that is either lower triangular or upper triangular. A matrix that is both upper and lower triangular is called a diagonal matrix.
Because matrix equations with triangular matrices are easier to solve, they are very important in numerical analysis. By the LU decomposition algorithm, an invertible matrix may be written as the product of a lower triangular matrix L and an upper triangular matrix U if and only if all its leading principal minors are non-zero.
- In the mathematical discipline of linear algebra, a triangular matrix is a special kind of square matrix. A square matrix is called lower triangular if all the entries above the main diagonal are zero. Similarly, a square matrix is called upper triangular if all the entries below the main diagonal are zero. A triangular matrix is one that is either lower triangular or upper triangular. A matrix that is both upper and lower triangular is called a diagonal matrix.