Orthogonal matrix
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Revision 2447
8/27/2026, 7:50:58 PM · Ancient Tree
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Revision 389
7/10/2026, 1:45:02 PM · Ancient Tree
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Recorded titleOrthogonal matrix
Recorded typeDefinition
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Revision 388
7/10/2026, 1:44:03 PM · Ancient Tree
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1
A squared real matrix $A$ is said orthogonal if it satisfies the equality $A\,A^{T}=A^{T}\,A=I_{n}$ where $A^{T}:=(a_{j,i})_{i,j}$ is the transposition of $A$.1
An orthogonal matrix is a real [[Square matrix|square matrix]] $A\in M_{n}(\R)$ satisfying2
$$A\,A^{T}=A^{T}\,A=I_{n}$$3
where $A^{T}$ is the [[Transpose of a matrix|transpose]] of $A$.Revision 356
7/8/2026, 6:14:16 PM · Sequoia
Concept created
A squared real matrix $A$ is said orthogonal if it satisfies the equality $A\,A^{T}=A^{T}\,A=I_{n}$ where $A^{T}:=(a_{j,i})_{i,j}$ is the transposition of $A$.