(data structure)

**Definition:**
A *matrix* that is only defined at (i,j) when i ≤ j.

**Generalization** (I am a kind of ...)

*matrix*.

**Specialization** (... is a kind of me.)

*strictly upper triangular matrix*, .

**See also**
*lower triangular matrix*, *ragged matrix*.

*Note:
For example *

j | ||||
---|---|---|---|---|

i | 1 | 7 | 7 | 6 |

- | 9 | 1 | 1 | |

- | - | 8 | 8 | |

- | - | - | 1 |

* It may be more compactly represented in an array by storing entry (i,j) in location n(i-1) + j - i(i-1)/2 = (2n-i)(i-1)/2 + j one-based indexing.*

Author: PEB

Go to the Dictionary of Algorithms and Data Structures home page.

If you have suggestions, corrections, or comments, please get in touch with Paul Black.

Entry modified 17 December 2004.

HTML page formatted Mon Feb 2 13:10:40 2015.

Cite this as:

Paul E. Black, "upper triangular matrix", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 17 December 2004. (accessed TODAY)
Available from: http://www.nist.gov/dads/HTML/upperTriangularMatrix.html