column vector: meaning, definition, pronunciation and examples
C2Technical / Academic
Quick answer
What does “column vector” mean?
A matrix consisting of a single column of numbers or elements, often used to represent a point or direction in space.
Audio
Pronunciation
Definition
Meaning and Definition
A matrix consisting of a single column of numbers or elements, often used to represent a point or direction in space.
In mathematics and physics, a one-dimensional vertical array of quantities (scalars) that obeys specific transformation rules; fundamental in linear algebra for representing vectors in coordinate systems.
Dialectal Variation
British vs American Usage
Differences
No significant lexical or conceptual differences. Spelling of related terms may differ (e.g., 'linearise' vs. 'linearize').
Connotations
Identical technical connotations in both varieties.
Frequency
Equally frequent in academic and engineering contexts in both regions.
Grammar
How to Use “column vector” in a Sentence
The vector v is a [adjective] column vector.Express the coordinates as a column vector.The matrix A multiplies the column vector x.Vocabulary
Collocations
Examples
Examples of “column vector” in a Sentence
adjective
British English
- The column-vector representation is more conventional here.
American English
- We need a column-vector format for the input.
Usage
Meaning in Context
Business
Virtually never used, except in highly specialised quantitative finance or data science roles.
Academic
Core term in mathematics, physics, computer science, and engineering lectures and textbooks.
Everyday
Not used in everyday conversation.
Technical
Essential term in linear algebra, machine learning, computational physics, and any field using matrix operations.
Vocabulary
Antonyms of “column vector”
Watch out
Common Mistakes When Using “column vector”
- Pronouncing 'column' as /kəʊˈluːm/ (like 'colume').
- Confusing it with a row vector by writing elements horizontally without transpose notation.
- Using the term in non-mathematical contexts.
FAQ
Frequently Asked Questions
Yes, a column vector is a specific type of matrix with dimensions n x 1 (n rows and 1 column).
It is often written with square or round brackets, with elements stacked vertically or separated by commas or semicolons within a single bracket, e.g., [1; 2; 3] or (1, 2, 3)^T where T denotes transpose.
Orientation. A column vector is vertical (n rows, 1 column), while a row vector is horizontal (1 row, n columns). They are transposes of each other.
Absolutely. Column vectors in advanced mathematics and physics frequently contain complex numbers.
A matrix consisting of a single column of numbers or elements, often used to represent a point or direction in space.
Column vector is usually technical / academic in register.
Column vector: in British English it is pronounced /ˈkɒləm ˈvɛktə/, and in American English it is pronounced /ˈkɑːləm ˈvɛktər/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Think of a Greek or Roman architectural column standing upright. A column vector is a vertical stack of numbers, just like a column.
Conceptual Metaphor
VECTOR AS AN ARROW / LIST; DATA AS A PHYSICAL OBJECT WITH ORIENTATION (vertical).
Practice
Quiz
What is the result of transposing a column vector?