query: Orthogonal tranformation over invariant subspace
positive_passages.docid: 22297
positive_passages.text: Normal operator $\Rightarrow$ S invariant implies $S^\perp$ invariant
negative_passages.docid: 137180
negative_passages.text: Orthonormal basis with specific norm
negative_passages.docid: 19946
negative_passages.text: Let $W$ be a given subspace of $V$ find the orthogonal complement $W^{\perp}$
negative_passages.docid: 34489
negative_passages.text: Matrix representation of linear transformation
negative_passages.docid: 43685
negative_passages.text: Generalized rotation matrix in N dimensional space around N-2 unit vector
negative_passages.docid: 127882
negative_passages.text: Proofs involving orthonormal basis
negative_passages.docid: 114309
negative_passages.text: T-invariant linear independence
negative_passages.docid: 112362
negative_passages.text: fixed point problem for orthogonal transformation
negative_passages.docid: 121047
negative_passages.text: Proof: Sum of dimension of orthogonal complement and vector subspace
negative_passages.docid: 10715
negative_passages.text: Orthogonal projection and two subspaces
negative_passages.docid: 32420
negative_passages.text: A complete orthonormal system contained in a dense sub-space.
negative_passages.docid: 121495
negative_passages.text: Decompose vector fields on product manifolds
negative_passages.docid: 18205
negative_passages.text: Orthogonal Projection
negative_passages.docid: 112376
negative_passages.text: ImageTransformation: polar to cartesian
negative_passages.docid: 114524
negative_passages.text: Proof Verification: the orthogonal complement of the column space is the left nullspace
negative_passages.docid: 66092
negative_passages.text: Simultaneous diagonalization of commuting linear transformations
negative_passages.docid: 72375
negative_passages.text: Efficiently Constructing Rank One Approximations for a Matrix using SVD