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 ..., 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 ... ,(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 ..., Prove that if A is an orthogonal matrix, the determinant of A is either 1 or -1., Theorem. Let Q be an orthogonal matrix. Then: detQ=±1. where detQ is the determinant of Q. Proof. By Determinant of Transpose: detQ⊺=detQ.
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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 [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 ... https://medium.com Orthogonal matrix - Wikipedia
https://en.wikipedia.org 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 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 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 ... https://math.stackexchange.com Orthogonal Matrices - Math Forum - Ask Dr. Math
Prove that if A is an orthogonal matrix, the determinant of A is either 1 or -1. http://mathforum.org 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 |