query: To what is $P (a\times b)$ equal when $P$ is orthogonal?
positive_passages.docid: 25335
positive_passages.text: Orthogonal matrix over cross product
negative_passages.docid: 128835
negative_passages.text: Compactness of the set of $n \times n$ orthogonal matrices
negative_passages.docid: 69497
negative_passages.text: Show that the set of all $n \times n$ orthogonal matrices, $O(n)$, is a compact subset of $\mbox{GL} (n,\mathbb R)$
negative_passages.docid: 148595
negative_passages.text: Find Orthogonal complement
negative_passages.docid: 6960
negative_passages.text: Necessary and sufficient condition for the matrix $A = I - 2 x x^t$ to be orthogonal
negative_passages.docid: 154628
negative_passages.text: What should we understand from the definition of orthogonality in inner product spaces other than $\mathbb R^n$?
negative_passages.docid: 79165
negative_passages.text: How to show that $P(A\cup B) = P(A) + P(B) - P(A\cap B)$
negative_passages.docid: 1962
negative_passages.text: Polynomial $P(a)=b,P(b)=c,P(c)=a$
negative_passages.docid: 93165
negative_passages.text: A projection satisfying $\| Px \| \leq \|x\|$ for all $x$ is an orthogonal projection
negative_passages.docid: 71245
negative_passages.text: $2 \times 2 $ Orthogonal Group
negative_passages.docid: 43219
negative_passages.text: If $[K(\alpha):K]=p\neq q=[K(\beta):K]$ then $[K(\alpha+\beta):K]=pq$
negative_passages.docid: 45179
negative_passages.text: When does the isomorphism $G\simeq \ker(\phi)\times \operatorname{im}(\phi)$? hold?
negative_passages.docid: 26861
negative_passages.text: $a+b=c \times d$ and $a\times b = c + d$
negative_passages.docid: 69980
negative_passages.text: Proving that if $A$ is an $n\times n$ orthogonal matrix, then $\det(A) = \pm1$
negative_passages.docid: 150166
negative_passages.text: What is $P([a_1,b_1]\times [a_2,b_2]\times...\times[a_k,b_k])$
negative_passages.docid: 54791
negative_passages.text: Is it true or false that $\lvert P([0, 1]) \setminus P((0, 1)) \rvert > \lvert P(\mathbb{N}) \rvert$
negative_passages.docid: 84522
negative_passages.text: A better proof for $\det(P) = \pm1$ if $P$ is an orthogonal matrix