query: Characterisation of the orthogonal projection
positive_passages.docid: 18205
positive_passages.text: Orthogonal Projection
negative_passages.docid: 69474
negative_passages.text: Orthogonal projections with $\sum P_i =I$, proving that $i\ne j \Rightarrow  P_{j}P_{i}=0$
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: 63465
negative_passages.text: Orthogonal Projection of $ z $ onto the Affine set $ \left\{ x \mid A x = b \right\} $
negative_passages.docid: 42606
negative_passages.text: Orthogonality for Binomial Coefficients
negative_passages.docid: 25335
negative_passages.text: Orthogonal matrix over cross product
negative_passages.docid: 88013
negative_passages.text: injective linear transformation basis.
negative_passages.docid: 20856
negative_passages.text: Inverse of Linear Transformations
negative_passages.docid: 48579
negative_passages.text: How to find the orthogonal complement of a subspace?
negative_passages.docid: 97994
negative_passages.text: Orthogonality Relations Exercise, Brezis' Book Functional Analysis
negative_passages.docid: 37060
negative_passages.text: The Parallelogram Identity for an inner product space
negative_passages.docid: 17517
negative_passages.text: Efficient implementation of tensorial Rayleigh product
negative_passages.docid: 153028
negative_passages.text: Showing that the product of vector magnitudes is larger than their dot product
negative_passages.docid: 129549
negative_passages.text: Showing that the orthogonal projection in a Hilbert space is compact iff the subspace is finite dimensional
negative_passages.docid: 60069
negative_passages.text: Orthogonal parametrization
negative_passages.docid: 156922
negative_passages.text: Proving convergence iff projection converges in product topology
negative_passages.docid: 56083
negative_passages.text: Find the eigenvalues of a projection operator