# Questions tagged [orthogonality]

This tag can be used to refer to the orthogonality of a set of vectors, a matrix or a linear transformation.

2,602 questions
Filter by
Sorted by
Tagged with
22 views

### How to make the gradient for a negative in triplet loss move ortogonal to the anchor and positive?

So i've implemented a convolutional neural network in C++ and I'm playing around with loss functions and gradient calculations. The network outputs the f(a), f(p) and f(n) of the last layer, which is ...
25 views

### How to choose a vector which is linearly independent from a set of orthogonal vectors?

I have a non-complete set of orthogonal vectors $V=[\mathbf{v}_1,\mathbf{v}_2,\ldots,\mathbf{v}_n]$ with $m > n$ entries. I would like to choose another vector $\mathbf{w}$ which is linearly ...
39 views

1 vote
26 views

65 views

### Hausdorff Distance Between Orthogonal Complements

Let $H$ be a finite-dimensional complex Hilbert space and denote by $d_{\textrm{Haus}}$ the Hausdorff distance between linear subspaces of $H$ i.e., $d_{\textrm{Haus}}(V,W)$ is the usual Hausdorff ...
I have a symmetric full rank matrix M, and a set of vectors $v_i$ that span the whole space. I assume those vectors to be orthogonal (they form an orthogonal set). If two of those vectors $v_i$ and \$...