orthogonal matrix determinant

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orthogonal matrix determinant

Note that det(A−I)=det(A−AA⊤)(∗)=det(I−A⊤)=(−1)ndet(A⊤−I)=(−1)ndet(A−I),. where in (∗) we use that det(A)=1. This means that if n is ..., Theorem. Let Q be an orthogonal matrix. Then: detQ=±1. where detQ is the determinant of Q. Proof. By Determinant of Transpose: detQ⊺=detQ., Prove that if A is an orthogonal matrix, the determinant of A is either 1 or -1.,(5)The determinant of an orthogonal matrix is equal to 1 or -1. The reason is that, since det(A) = det(At) for any A, and the determinant of the product is the ... , , Not sure what's wrong with using the transpose, but here it goes. Since Q is orthogonal, QQT=I=QTQ by definition. Using the fact that ..., The determinant of an orthogonal matrix is equal to 1 or -1. Since det(A) = det(Aᵀ) and the determinant of product is the product of determinants ...,在矩陣論中,正交矩陣(英語:orthogonal matrix)是一個方塊矩陣 Q -displaystyle Q} Q ,其元素為實數,而且行向量與列向量皆為正交的單位向量,使得該矩陣 ...

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orthogonal matrix determinant 相關參考資料
determinant of an orthogonal matrix - Mathematics Stack ...

Note that det(A−I)=det(A−AA⊤)(∗)=det(I−A⊤)=(−1)ndet(A⊤−I)=(−1)ndet(A−I),. where in (∗) we use that det(A)=1. This means that if n is ...

https://math.stackexchange.com

Determinant of Orthogonal Matrix is Plus or Minus One ...

Theorem. Let Q be an orthogonal matrix. Then: detQ=±1. where detQ is the determinant of Q. Proof. By Determinant of Transpose: detQ⊺=detQ.

https://proofwiki.org

Orthogonal Matrices - Math Forum - Ask Dr. Math

Prove that if A is an orthogonal matrix, the determinant of A is either 1 or -1.

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ORTHOGONAL MATRICES Informally, an orthogonal n × n ...

(5)The determinant of an orthogonal matrix is equal to 1 or -1. The reason is that, since det(A) = det(At) for any A, and the determinant of the product is the ...

http://www.math.utk.edu

Orthogonal matrix - Wikipedia

https://en.wikipedia.org

Show that any orthogonal matrix has determinant 1 or -1 ...

Not sure what's wrong with using the transpose, but here it goes. Since Q is orthogonal, QQT=I=QTQ by definition. Using the fact that ...

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[Linear Algebra] 9. Properties of orthogonal matrices | by Jun ...

The determinant of an orthogonal matrix is equal to 1 or -1. Since det(A) = det(Aᵀ) and the determinant of product is the product of determinants ...

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正交矩陣- 維基百科,自由的百科全書 - Wikipedia

在矩陣論中,正交矩陣(英語:orthogonal matrix)是一個方塊矩陣 Q -displaystyle Q} Q ,其元素為實數,而且行向量與列向量皆為正交的單位向量,使得該矩陣 ...

https://zh.wikipedia.org