secondary diagonal: meaning, definition, pronunciation and examples
C2technical, academic
Quick answer
What does “secondary diagonal” mean?
The diagonal line running from the top-right corner to the bottom-left corner of a square matrix or geometric figure.
Audio
Pronunciation
Definition
Meaning and Definition
The diagonal line running from the top-right corner to the bottom-left corner of a square matrix or geometric figure.
In matrices, the set of entries where the row and column indices sum to n+1 (for an n×n matrix). In geometry, the diagonal connecting non-adjacent vertices that is not the main or primary diagonal.
Dialectal Variation
British vs American Usage
Differences
No significant lexical differences. The term is identical in both varieties within technical contexts.
Connotations
Purely technical, no cultural or connotative differences.
Frequency
Equally rare and specialized in both dialects, confined to mathematics education and professional fields.
Grammar
How to Use “secondary diagonal” in a Sentence
The secondary diagonal of [MATRIX/FIGURE] is...Calculate [PROPERTY] for the secondary diagonal.Elements/Elements on the secondary diagonal are...Vocabulary
Collocations
Examples
Examples of “secondary diagonal” in a Sentence
verb
British English
- (Not applicable as a verb)
American English
- (Not applicable as a verb)
adverb
British English
- (Not applicable as an adverb)
American English
- (Not applicable as an adverb)
adjective
British English
- The secondary-diagonal elements were all zero.
- We examined its secondary-diagonal properties.
American English
- The secondary-diagonal entries sum to five.
- A secondary-diagonal matrix has non-zero elements only on that line.
Usage
Meaning in Context
Business
Virtually never used. Hypothetically, in advanced data analysis involving correlation matrices.
Academic
Core term in linear algebra, matrix theory, and geometry courses.
Everyday
Extremely rare. Might be used in puzzles (e.g., Sudoku, magic squares).
Technical
Primary context. Used in mathematics, computer graphics, physics, and engineering when dealing with matrices.
Vocabulary
Synonyms of “secondary diagonal”
Strong
Neutral
Weak
Vocabulary
Antonyms of “secondary diagonal”
Watch out
Common Mistakes When Using “secondary diagonal”
- Confusing it with the main diagonal. Using it for non-square rectangles. Misidentifying the direction (top-right to bottom-left is fixed).
FAQ
Frequently Asked Questions
Yes, in mathematics, particularly linear algebra, 'antidiagonal' is a direct synonym for 'secondary diagonal'.
Technically, the term is defined for squares (matrices or geometric squares). For a rectangle, one might refer to the 'diagonal from the top-right to bottom-left', but 'secondary diagonal' is not standardly used.
For an n x n matrix, if an element is on the secondary diagonal, its row index (i) and column index (j) satisfy the equation i + j = n + 1.
No. The trace is defined specifically as the sum of the elements on the main diagonal (top-left to bottom-right), not the secondary diagonal.
The diagonal line running from the top-right corner to the bottom-left corner of a square matrix or geometric figure.
Secondary diagonal is usually technical, academic in register.
Secondary diagonal: in British English it is pronounced /ˈsɛkənd(ə)ri ˌdaɪˈæɡənəl/, and in American English it is pronounced /ˈsɛkənˌdɛri daɪˈæɡənəl/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “(No established idioms; it is a technical term.)”
Learning
Memory Aids
Mnemonic
Think of a square. The main diagonal goes from the top-left 'home' corner. The SECONDARY one is the 'guest' route from top-right to bottom-left.
Conceptual Metaphor
A 'secondary road' or 'back route' across a structured grid, as opposed to the main highway of the primary diagonal.
Practice
Quiz
In which field is the term 'secondary diagonal' most precisely defined and commonly used?