Prev: ANN
Next: Choosing elements from returned array
From: Me on 9 Jul 2010 02:15
Given a column vector v is it possible to express, using "traditional"
linear algebra operators/notation, the matrix which contains the
elements of v along the diagonal, and all other elements zero?

I essentially want what Matlab would produce with "diag(v)" but
expressed as a matrix/vector equation.

Thanks, Dave
From: Rune Allnor on 9 Jul 2010 05:46
On 9 Jul, 08:15, Me <The...(a)Ours.CC> wrote:
> Given a column vector v is it possible to express, using "traditional"
> linear algebra operators/notation, the matrix which contains the
> elements of v along the diagonal, and all other elements zero?
>
> I essentially want what Matlab would produce with "diag(v)" but
> expressed as a matrix/vector equation.

Don't think it can be done.

Assume v is N x 1 with all non-zero coefficients. The only way
to produce a N x N matrix X from v is to right multiply with
a 1 x N vector u:

X = vu [1]

As far as I can tell, X will have a non-zero column everywhere
u has a non-zero coeffcient. Which means the vector product [1]
can not produce a diagonal matrix. Which in turn means that
what you ask can not be done.

Rune
From: Bruno Luong on 9 Jul 2010 06:58
Me <Theirs(a)Ours.CC> wrote in message <i16epf$c0b$1(a)news.eternal-september.org>...
> Given a column vector v is it possible to express, using "traditional"
> linear algebra operators/notation, the matrix which contains the
> elements of v along the diagonal, and all other elements zero?
>
> I essentially want what Matlab would produce with "diag(v)" but
> expressed as a matrix/vector equation.
>
> Thanks, Dave

M = diag(v) can be defined as the matrix (in canonic basic) of the linear operator

x -> v \centerdot x for all x in R^n,

Where \centerdot is the big centered bullet used for Schur's product (or called alternatively by Hadamard's or pointwise): http://www.ee.ic.ac.uk/hp/staff/dmb/matrix/relation.html

Bruno
From: TCL on 9 Jul 2010 09:16
On Jul 9, 2:15 am, Me <The...(a)Ours.CC> wrote:
> Given a column vector v is it possible to express, using "traditional"
> linear algebra operators/notation, the matrix which contains the
> elements of v along the diagonal, and all other elements zero?
>
> I essentially want what Matlab would produce with "diag(v)" but
> expressed as a matrix/vector equation.
>
> Thanks, Dave

Say your vector v is nx1 vector. Let e_i be the i-th unit column
vector. Then the matrix you want is

Sum ( (v^t e_i)e_i e_i^t, i=1,..,n )

-TCL
From: Matt J on 9 Jul 2010 10:34
Me <Theirs(a)Ours.CC> wrote in message <i16epf$c0b$1(a)news.eternal-september.org>...
> Given a column vector v is it possible to express, using "traditional"
> linear algebra operators/notation, the matrix which contains the
> elements of v along the diagonal, and all other elements zero?
>
> I essentially want what Matlab would produce with "diag(v)" but
> expressed as a matrix/vector equation.
============

I don't know if this is precisely what you're looking for, but you can define your own customized linear operator using

http://www.mathworks.com/matlabcentral/fileexchange/26611-on-the-fly-definition-of-custom-matrix-objects

For you, this would be something like the following,

>> A=MatrixObj; A.Ops.mtimes=@(A,v) diag(v);

>> A*[1;2;3]

ans =

1 0 0
0 2 0
0 0 3
 | 
Pages: 1
Prev: ANN
Next: Choosing elements from returned array