Diagonal matrix

Algebra

In linear algebra, a diagonal matrix is a matrix whose entries outside the main diagonal are all zero, usually a square matrix. Its main-diagonal elements may be zero or nonzero. Identity matrices and their multiples are diagonal matrices, with multiples of an identity matrix called scalar matrices. In geometry, diagonal matrices can serve as scaling matrices, changing size and possibly shape through matrix multiplication. Only scalar matrices produce uniform scaling.

The picture on this card was made with AI. It is an illustration, not a real photo of the subject.

Definition: Entries outside the main diagonal are zero.
Main diagonal: Elements may be zero or nonzero.
Uniform scaling: Only scalar matrices result in uniform scale change.

Sources and credits

Article: Diagonal matrix (English Wikipedia)
Wikidata: Q332791
Text: Card text is adapted from the English Wikipedia article by an automated summary. Wikipedia content is available under CC BY-SA 4.0; see the article history for its contributors. CC BY-SA 4.0 · Article history and contributors
Illustration: AI-generated illustration. Not a photograph or documentary image. (model: gpt-image-2.5-flare)
Popularity: 80 median daily views (Wikimedia Pageviews API (all-access, user agent))

Kosmora is not affiliated with or endorsed by the Wikimedia Foundation.