Definition

To change a square matrix into a diagonal matrix by using another matrix and its inverse, so that all the nonzero elements are arranged from the upper left to the lower right.

Example

In linear algebra, we often diagonalize matrices to simplify calculations.

Tense Forms

Conversation

Have you learned how to diagonalize matrices yet?

Not yet, but I heard it's really important for linear algebra.

Yeah, it makes solving equations so much easier once you can diagonalize them.

I can’t wait to understand it better; it sounds really useful.

Synonyms & Antonyms

Root Explanation

Diagonalize → It is formed from "dia-" (meaning across) and "gonia" (from Greek "gonia", meaning angle). The word "diagonalize" means to transform something in a way that relates to angles across a figure, typically in mathematics.

Memory Tip

Think of 'across' ('dia-') and 'angle' ('gonia') to remember that 'diagonalize' involves transforming something across angles.

Visually Confused Words