Mathematics for AI and Machine Learning

Foundations for modern AI and machine learning

Orthonormal Inverse

Chapter 3 Linear algebra

Chapter 3: Subspaces and Orthogonality — Props & Inverses

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Orthonormal Inverse — high-resolution mind-map icon

From the book

Chapter 3: Subspaces and Orthogonality. In the chapter mind map this icon labels Props & Inverses. The discussion below is excerpted and lightly edited from § Opening in Mathematics for AI and Machine Learning.

Four fundamental subspaces and orthonormal matrices: rank-nullity theorem and orthogonality relationships

What this drawing shows

What you see. Represents the fact that an orthonormal matrix inverts by transposition, preserving lengths and angles.

In the mind map. Chapter 3 — Props & Inverses. See From the book above for definitions, figures, and worked examples.

Where to read next

Open Chapter 3 companion →

Read the full definitions, figures, and worked examples in Chapter 3: Subspaces and Orthogonality — see the mind-map node Props & Inverses.