triangular matrix: meaning, definition, pronunciation and examples
LowAcademic, Technical (Mathematics, Computer Science, Engineering)
Quick answer
What does “triangular matrix” mean?
A square matrix in which all the entries either above or below the main diagonal are zero.
Audio
Pronunciation
Definition
Meaning and Definition
A square matrix in which all the entries either above or below the main diagonal are zero.
In linear algebra, a matrix where all elements on one side of the main diagonal are zero; can be upper triangular (non-zero entries on/above diagonal) or lower triangular (non-zero entries on/below diagonal). The term can be metaphorically used in other fields to describe a triangular structure or a three-way relationship.
Dialectal Variation
British vs American Usage
Differences
No significant differences in definition or usage. Spelling of related terms may differ (e.g., 'factorise' vs. 'factorize').
Connotations
None beyond its technical meaning.
Frequency
Equal frequency in both dialects within relevant technical fields; extremely rare in general discourse.
Grammar
How to Use “triangular matrix” in a Sentence
[verb] + a/the + triangular matrix (e.g., compute, invert, store)triangular matrix + [preposition] + [noun] (e.g., decomposition of, algorithm for)[adjective] + triangular matrix (e.g., sparse, block)Vocabulary
Collocations
Examples
Examples of “triangular matrix” in a Sentence
verb
British English
- The algorithm will triangularise the matrix for efficient solving.
- We need to triangularise this system of equations.
American English
- The algorithm will triangularize the matrix for efficient solving.
- We need to triangularize this system of equations.
adverb
British English
- The data was stored triangularly to save memory.
- The elements are arranged triangularly in the array.
American English
- The data was stored triangularly to save memory.
- The elements are arranged triangularly in the array.
Usage
Meaning in Context
Business
Virtually never used. Potentially in highly technical finance or data analytics roles discussing specific computational methods.
Academic
Core term in linear algebra, numerical analysis, and related STEM fields. Used in lectures, textbooks, and research papers.
Everyday
Extremely rare. Unlikely to be encountered outside of specific educational or professional technical contexts.
Technical
Primary domain of use. Essential in mathematics, computer science (algorithms), engineering (computations), and data science.
Vocabulary
Synonyms of “triangular matrix”
Weak
Vocabulary
Antonyms of “triangular matrix”
Watch out
Common Mistakes When Using “triangular matrix”
- Using 'triangular matrix' to refer to any non-square matrix (it must be square).
- Confusing 'upper' and 'lower' triangular.
- Mispronouncing 'triangular' with four syllables (e.g., /traɪˌæŋɡjʊlər/) as opposed to the common three-syllable /traɪˌæŋɡjələr/ in American English.
FAQ
Frequently Asked Questions
Yes, by the standard definition in linear algebra, a triangular matrix is always a square matrix.
An upper triangular matrix has non-zero entries only on or above the main diagonal (zeros below). A lower triangular matrix has non-zero entries only on or below the main diagonal (zeros above).
They are computationally efficient. Solving systems of linear equations (forward/back substitution) and calculating determinants become much simpler and faster when working with triangular matrices.
Yes. A diagonal matrix is both an upper and a lower triangular matrix simultaneously, as all entries both above and below the main diagonal are zero.
A square matrix in which all the entries either above or below the main diagonal are zero.
Triangular matrix is usually academic, technical (mathematics, computer science, engineering) in register.
Triangular matrix: in British English it is pronounced /traɪˌæŋɡjʊlə ˈmeɪtrɪks/, and in American English it is pronounced /traɪˌæŋɡjələr ˈmeɪtrɪks/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Think of a **triangle** drawn over a grid (matrix). The zeros fill one corner of the triangle, leaving the other part (including the diagonal) potentially non-zero.
Conceptual Metaphor
A LAYERED HIERARCHY or a FUNNEL (as operations often proceed efficiently from one corner). A CLEAN SLATE in one half (the zero entries).
Practice
Quiz
What is a defining property of a triangular matrix?