(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 1-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 16 November 2016.

HTML page formatted Fri Feb 23 10:06:08 2018.

Cite this as:

Paul E. Black, "upper triangular matrix", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 16 November 2016. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/upperTriangularMatrix.html