Mathematics for AI and Machine Learning

Foundations for modern AI and machine learning

Covariance

Chapter 13 Probability & information

Chapter 13: Probability and Random Variables — Cov Matrices

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Covariance — high-resolution mind-map icon

From the book

Chapter 13: Probability and Random Variables. In the chapter mind map this icon labels Cov Matrices. The discussion below is excerpted and lightly edited from § Definition: Covariance in Mathematics for AI and Machine Learning.

For random variables $X \in \mathbb{R}$ and $Y \in \mathbb{R}$, the covariance is defined as

What this drawing shows

What you see. Represents how variables vary together and how probability mass stretches along correlated directions.

In the mind map. Chapter 13 — Cov Matrices. See From the book above for definitions, figures, and worked examples.

Where to read next

Open Chapter 13 companion →

Read the full definitions, figures, and worked examples in Chapter 13: Probability and Random Variables — see the mind-map node Cov Matrices.