diagonal matrix: meaning, definition, pronunciation and examples
C2Technical / Academic
Quick answer
What does “diagonal matrix” mean?
A square matrix in which all entries outside the main diagonal are zero.
Audio
Pronunciation
Definition
Meaning and Definition
A square matrix in which all entries outside the main diagonal are zero.
A matrix that represents a linear transformation that scales each coordinate axis independently, making it computationally simple. In non-technical contexts, it can metaphorically describe a situation with independent, non-interacting components.
Dialectal Variation
British vs American Usage
Differences
No lexical or semantic differences. Spelling of related terms may follow regional conventions (e.g., 'linearisation' vs. 'linearization').
Connotations
Identical technical meaning. No cultural or connotative differences.
Frequency
Equally frequent in academic mathematics and engineering contexts in both regions.
Grammar
How to Use “diagonal matrix” in a Sentence
The matrix [Subject] is diagonal.They decomposed it into [Object] a diagonal matrix and an orthogonal one.A diagonal matrix [Subject] with entries d_i.Vocabulary
Collocations
Examples
Examples of “diagonal matrix” in a Sentence
adjective
British English
- The diagonal matrix form simplifies the calculation.
American English
- The diagonal matrix form simplifies the calculation.
Usage
Meaning in Context
Business
Virtually never used, except in highly technical quantitative finance roles discussing covariance matrices.
Academic
Core term in mathematics, physics, computer science, engineering, and statistics lectures and publications.
Everyday
Extremely rare. Would only be used by someone explaining a technical concept to a layperson.
Technical
Fundamental term. Used constantly in linear algebra, numerical analysis, signal processing, quantum mechanics, and machine learning.
Vocabulary
Synonyms of “diagonal matrix”
Neutral
Weak
Vocabulary
Antonyms of “diagonal matrix”
Watch out
Common Mistakes When Using “diagonal matrix”
- Using 'diagonal matrix' to refer to any matrix with non-zero diagonal elements (must have zeros *everywhere else*).
- Confusing 'diagonal' with 'diagonalisable'.
- Forgetting it must be a square matrix.
FAQ
Frequently Asked Questions
Yes, by definition, a diagonal matrix is a square matrix where entries outside the main diagonal are zero.
They are computationally efficient. Multiplying a vector by a diagonal matrix is much faster than by a full matrix, as it only involves scaling each component.
Yes, the identity matrix is a special case of a diagonal matrix where all diagonal entries are 1.
Yes, diagonal entries can be any number, including zero. However, if a diagonal entry is zero, the matrix is singular (non-invertible).
A square matrix in which all entries outside the main diagonal are zero.
Diagonal matrix is usually technical / academic in register.
Diagonal matrix: in British English it is pronounced /ˌdaɪˈæɡ.ən.əl ˈmeɪ.trɪks/, and in American English it is pronounced /daɪˈæɡ.ən.əl ˈmeɪ.trɪks/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Imagine a fence with posts only on the diagonal line from the top-left corner to the bottom-right corner. All other squares are empty. That's a DIAGONAL MATRIX.
Conceptual Metaphor
INDEPENDENCE IS DIAGONALITY (e.g., 'The system's variables are uncoupled, resulting in a diagonal matrix of coefficients.')
Practice
Quiz
What is a key property of a diagonal matrix?