# Tagged Questions

For questions about vector spaces and their properties. More general questions about linear algebra belong under the [tag:linear-algebra] tag. A vector space is a space which consists of elements called "vectors", which can be added and multiplied by scalars. In other words, these are the spaces ...

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### If I have a vector inside a rectangle, how do I tell which side of the rectangle the vector will hit?

I'm trying to solve an issue where I basically have a vector inside of a rectangle. I want to figure out if the vector continues its trajectory, what side will it strike? The vector is given as an (x, ...
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### Is there a name for a $k$-sphere embedded in $\mathbb{R}^n$?

In my thesis in a lot of places there comes up a $k$-sphere embedded in $\mathbb{R}^n$. We call lower-dimensional "planes" in $\mathbb{R}^n$ linear manifolds or flats, is there also a term for a lower-...
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### Rule for $\langle x,y\rangle$ if we know orthonormal base?

How to define $\langle x,y \rangle$ in space of polinoms, where $1, x-1 , 1-x^2$ are orthonormal base($\Vert a\Vert = 1$, $\langle a1, a2\rangle = 0$)? I'm a bit lost, I know how to do it with my ...
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### A possible generalized determinant?

This will likely seem a bit contrived, and admittedly it is, but I wanted to see just how "close" we could get to generalizing the concept of a determinant. In what follows, we will lose quite a few ...
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### Question about Column space and Row space of generic matrix $A$ and the corresponding upper triangular $U$

I am doing the following exercise from Introduction to Linear Algebra: Find the dimensions of (a) the column space of A, (b) the column space of U , (c) the row space of A, (d) the row space of U ....
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### warping a cube in a 3d space

3D cube made with Octave The problem I have is shown in the picture above. I have 2 cubes where both cubes are filled with vectors, or have possible vector locations. The blue cube is filled normally,...
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