square matrix: meaning, definition, pronunciation and examples
C1-C2/Academic/TechnicalFormal academic, technical, and mathematical writing. Not used in casual conversation.
Quick answer
What does “square matrix” mean?
A rectangular array of numbers, symbols, or expressions arranged in rows and columns where the number of rows equals the number of columns.
Audio
Pronunciation
Definition
Meaning and Definition
A rectangular array of numbers, symbols, or expressions arranged in rows and columns where the number of rows equals the number of columns.
In a broader sense, it is a foundational concept in linear algebra representing linear transformations from a vector space to itself, a square arrangement of coefficients for a system of linear equations, or a key data structure in computer science. Its properties, such as the determinant, trace, and eigenvalues, are fundamental to many applications.
Dialectal Variation
British vs American Usage
Differences
No lexical differences. Potential minor differences in spoken emphasis ('square ma-trix' vs. 'square ma-trix').
Connotations
Identical technical connotations. Non-technical metaphorical use is rare in both varieties.
Frequency
Frequency is tied exclusively to technical/academic contexts and is identical in both regions.
Grammar
How to Use “square matrix” in a Sentence
The coefficient matrix for the system must be a [square matrix].Only a [square matrix] can have an inverse.We can compute the eigenvalues for any [square matrix].Vocabulary
Collocations
Examples
Examples of “square matrix” in a Sentence
noun
British English
- The algorithm specifically requires the input to be a square matrix.
- One key property of a square matrix is its trace.
American English
- You can only compute the determinant for a square matrix.
- The transformation is represented by a 3x3 square matrix.
Usage
Meaning in Context
Business
Rarely used directly. May appear in data science contexts, e.g., 'The correlation matrix is a square matrix of pairwise relationships.'
Academic
Core term in mathematics, physics, computer science, engineering, and economics. Used in proofs, problem sets, and theoretical discussions.
Everyday
Virtually never used.
Technical
Fundamental in algorithms, graphics (transformation matrices), statistics (covariance matrices), and systems theory.
Vocabulary
Synonyms of “square matrix”
Strong
Neutral
Weak
Vocabulary
Antonyms of “square matrix”
Watch out
Common Mistakes When Using “square matrix”
- Using 'square matrix' when referring to any matrix.
- Attempting to find the inverse of a non-square matrix.
- Confusing it with a 'magic square'.
FAQ
Frequently Asked Questions
No, by definition, a square matrix has an equal number of rows and columns (denoted as n x n).
Yes, the identity matrix is a square matrix with ones on the main diagonal and zeros elsewhere.
Square matrices represent linear transformations from a space to itself, allowing for concepts like eigenvalues, inverses, and determinants, which are crucial for solving systems of equations and analysing system behaviour.
No, only invertible (or non-singular) square matrices have inverses. A square matrix is singular if its determinant is zero, meaning it has no inverse.
A rectangular array of numbers, symbols, or expressions arranged in rows and columns where the number of rows equals the number of columns.
Square matrix is usually formal academic, technical, and mathematical writing. not used in casual conversation. in register.
Square matrix: in British English it is pronounced /skweə ˈmeɪ.trɪks/, and in American English it is pronounced /skwer ˈmeɪ.trɪks/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “To square the matrix (rare, meaning to ensure a matrix is square for an operation).”
Learning
Memory Aids
Mnemonic
Think of a square room: same length and width. A square matrix has the same number of rows (height) and columns (width).
Conceptual Metaphor
A SELF-CONTAINED SYSTEM; A BALANCED FOUNDATION (e.g., 'The governance model forms a square matrix of responsibilities').
Practice
Quiz
Which of the following operations is uniquely defined for a square matrix but not necessarily for a rectangular one?