All Questions

One encounters often in numerics non-square matrices with orthonormal columns, i.e., $U\in\mathbb{R}^{m\times n}$, with $m > n$, such that $U^TU=I$ (but, clearly, $UU^T \neq I$). Is there a name ...

Is there an established term for the following type of square matrices? $\begin{pmatrix} c & c & c & c & \cdots & c & c \\ c & a & b & b & \cdots & b & ...

What do you call a linear map of the form $\alpha X$, where $\alpha\in\Bbb R$ and $X\in\mathrm O(V)$ is an orthogonal map ($V$ being some linear space with inner product)? Are there established names, ...

What is the term for a matrix whose columns are mutually orthogonal, but not necessarily othonormal? I can't name such a matrix "orthogonal" because that would imply that all columns are unit vectors....