query: Finding the Basis for an Orthogonal Subspace
positive_passages.docid: 19946
positive_passages.text: Let $W$ be a given subspace of $V$ find the orthogonal complement $W^{\perp}$
negative_passages.docid: 48113
negative_passages.text: Find a basis for the vector space of symmetric matrices with an order of $n \times n$
negative_passages.docid: 42606
negative_passages.text: Orthogonality for Binomial Coefficients
negative_passages.docid: 115368
negative_passages.text: Diagonal Subspace of Cartesian Product
negative_passages.docid: 15811
negative_passages.text: Finding a basis for a certain vector space of periodic polynomials
negative_passages.docid: 117175
negative_passages.text: Proof that the 2-norm of orthogonal transformation of a matrix is invariant
negative_passages.docid: 145885
negative_passages.text: Linear transformation preserving orthogonality
negative_passages.docid: 18205
negative_passages.text: Orthogonal Projection
negative_passages.docid: 25335
negative_passages.text: Orthogonal matrix over cross 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: 51313
negative_passages.text: Extension of linearly independent set to a basis in an infinite dimensional vector space
negative_passages.docid: 137209
negative_passages.text: Finding the Matrix of a Linear Operator Satisfying a Polynomial
negative_passages.docid: 152742
negative_passages.text: Finding a basis of an infinite-dimensional vector space?
negative_passages.docid: 59192
negative_passages.text: Basis of cotangent space
negative_passages.docid: 30017
negative_passages.text: Orthogonality and linear independence
negative_passages.docid: 52888
negative_passages.text: Find all values of a for which $\{v_1,v_2,v_3\}$ form a basis for ${\bf R}^3$
negative_passages.docid: 148595
negative_passages.text: Find Orthogonal complement