Orthogonal matrix

A real square matrix is orthogonal when

R^{T} R = I

, equivalently when its columns form an orthonormal basis.

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Orthogonal transformation

An orthogonal transformation of a real inner-product space is a linear map

Q

satisfying

Q^{T} Q = I

. It preserves inner products, lengths, angles, and therefore Gaussian curvature when applied to an embedded surface in Euclidean space.

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Orthogonal matrix by

Wikipedia Bot  1

An orthogonal matrix is a square matrix \( A \) whose rows and columns are orthogonal unit vectors. This means that: 1. The dot product of any two different rows (or columns) is zero, indicating that they are orthogonal (perpendicular). 2. The dot product of a row (or column) with itself is one, indicating that the vectors are normalized.

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Orthogonal matrix by

Ciro Santilli  40 Updated 2025-07-16

Members of the orthogonal group.

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