query: What does it mean for two functions to be orthogonal?
positive_passages.docid: 154628
positive_passages.text: What should we understand from the definition of orthogonality in inner product spaces other than $\mathbb R^n$?
negative_passages.docid: 127000
negative_passages.text: When does $V = \ker(f) \oplus \operatorname{im}(f)$?
negative_passages.docid: 88153
negative_passages.text: Finding all inner products on $\mathbb{R}^2$ for which a given linear map is orthogonal
negative_passages.docid: 117175
negative_passages.text: Proof that the 2-norm of orthogonal transformation of a matrix is invariant
negative_passages.docid: 95319
negative_passages.text: What does this weird function definition mean?
negative_passages.docid: 36064
negative_passages.text: How many $3 \times 3$ integer matrices are orthogonal?
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: 44148
negative_passages.text: Functions that are their own inverse.
negative_passages.docid: 9436
negative_passages.text: How to define an orthogonal basis in the right way?
negative_passages.docid: 99221
negative_passages.text: Orthogonality lemma sine and cosine
negative_passages.docid: 60069
negative_passages.text: Orthogonal parametrization
negative_passages.docid: 109573
negative_passages.text: Is sum of two orthogonal matrices singular?
negative_passages.docid: 21366
negative_passages.text: Help on the relationship of a basis and a dual basis
negative_passages.docid: 37794
negative_passages.text: Proving the two given vectors are orthogonal
negative_passages.docid: 37985
negative_passages.text: Show that $|x|^2 = |y|^2$ with $A$ orthogonal and $Ax = \cos (θ)x − \sin (θ)y$, $Ay = \sin (θ)x + \cos (θ) y$
negative_passages.docid: 108505
negative_passages.text: Matrix Concentration for Products- Orthogonality Property
negative_passages.docid: 141015
negative_passages.text: Proof of orthogonal matrix