Mathematics for AI and Machine Learning

Foundations for modern AI and machine learning

Diagonal Matrix

Chapter 2 Linear algebra

Chapter 2: Matrix — Diagonal (also appears in Ch. 5, Ch. 5)

High-resolution PNG
Diagonal Matrix — high-resolution mind-map icon

From the book

Chapter 2: Matrix. In the chapter mind map this icon labels Diagonal. The discussion below is excerpted and lightly edited from § Definition: Diagonal Matrix in Mathematics for AI and Machine Learning. Related material also appears in Chapter 5 (Trace & Cyclic Props), Chapter 5 (Determinants & Inverses via LU).

That is, all off-diagonal entries are zero. A diagonal matrix has the form:

Notation: We often write $\text{diag}(d_0, d_1, \ldots, d_{N-1})$ to denote a diagonal matrix with diagonal entries $d_0, d_1, \ldots, d_{N-1}$.

What this drawing shows

What you see. Square matrix whose nonzero structure lies on the main diagonal, representing independent coordinate scaling.

In the mind map. Chapter 2 — Diagonal. See From the book above for definitions, figures, and worked examples.

Also appears in Ch. 5 (Trace & Cyclic Props); Ch. 5 (Determinants & Inverses via LU).

Where to read next

Open Chapter 2 companion →

Read the full definitions, figures, and worked examples in Chapter 2: Matrix — see the mind-map node Diagonal.

This concept is also referenced in Chapter 5 (Trace & Cyclic Props); Chapter 5 (Determinants & Inverses via LU).