What does "diagonalize" mean?

To convert a square matrix into a diagonal matrix by multiplying it by a second matrix and its inverse.

What is a synonym for "diagonalize"?

Common synonyms include: cut, cut across, diagonalise, slant, slash.

Diagonalize

verb

verb ·Rare ·Advanced level

Definitions

Verb

1
To convert a square matrix into a diagonal matrix by multiplying it by a second matrix and its inverse. transitive
2
transform a matrix to a diagonal matrix wordnet
3
To design variables such that design problems only bear upon subsets that are loosely coupled to others.
"And what we should do, therefore, is to diagonalize the variables—we should find some new design variables such that design problems only bear upon subsets of them that are loosely coupled to others, like the subsystems of ten lights in the example."

Synonyms

All synonyms

cut cut across diagonalise slant slash

Example

More examples

"And what we should do, therefore, is to diagonalize the variables—we should find some new design variables such that design problems only bear upon subsets of them that are loosely coupled to others, like the subsystems of ten lights in the example."

Etymology

From diagonal + -ize.

Related phrases

diagonal matrix square matrix

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Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.