Matrix Representation of a Uniform Sphere Centered at the Origin

[PhysicsChode]

What is the basic matrix form for a uniform (unit) sphere centered at the origin? Given a vector that specifies the radii (1,1,1) == (r1,r2,r3), I would like the matrix that implies no rotation (is it [[1,0,0],[0,1,0],[0,0,1]]?) and covers the rest of the necessary parameters.
I am testing ellipsoid-plotting code, and I also welcome any other matrices useful for testing.

 

[BvU]

Hello PC,

What is it you expect from a matrix to describe a sphere ? On what will you turn loose such a matrix ?
I know of matrices that represent a rotation about a given axis, but you probably know that too.

 

[PhysicsChode]

The matrix I'm asking for, combined with a 3-vector for the 3 perpendicular radii of the ellipsoid (in this case a sphere) produces an ellipsoid with a rotation specified by the matrix.

 

[BvU]

A matrix on a vector produces a vector, not an ellipsoid. So I still don't get it. Or do you want variables in there ? Like in wiki rotation matrix which I hope you checked already.

 

[Declun]

I was thinking about vectors as well in the matrix. However, if space and time bend.. Perhaps you can achieve a spherical shape, that looks like vectors. Take a pyramid for instance.. when you look at it one way its a pyramid, and another way it can look completely different such as a triangle from a 2d perspective. Perhaps you can see a sphere the same way, in vectors or different dimensions?

 

[BvU]

Funny thing about a sphere is that it looks the same, no matter from where you look at it. I think even when you manage to move relative to the thing with a speed that is a considerable fraction of the light speed (but I could be a bit wrong there) .

But you have something in mind I can't fathom yet: testing plotting code that receives a matrix as input ? What's it look like ?

And if you think space and time bend, what am I to make of that ?

 

[HallsofIvy]

I was thinking about vectors as well in the matrix. However, if space and time bend.. Perhaps you can achieve a spherical shape, that looks like vectors. Take a pyramid for instance.. when you look at it one way its a pyramid, and another way it can look completely different such as a triangle from a 2d perspective. Perhaps you can see a sphere the same way, in vectors or different dimensions?

Frankly, what you are saying (for example "Perhaps you can achieve a spherical shape, that looks like a line") makes me think you are using words that you don't understand. A sphere has the property that, looked at from any angle, it still looks like a sphere. However, there is NO three dimensional object such that, looked at from a specific angle, looks like a line.