Can someone with access to an ISO standard APL
(say Dyalog APL) tell me whether the monad matrix
inverse (domino) gives a result on wide matrices?
The following expression should either always
signal an error, or nearly always produce 13 7
{rho} {domino} ? 7 13 {rho} 1e6
Execute the expression at least twice in case we are
extremely unlucky with the random numbers.
----- Original Message -----
From: Roger Hui <[EMAIL PROTECTED]>
Date: Friday, September 7, 2007 13:23
Subject: Re: [Jgeneral] linear independence?
To: General forum <[email protected]>
> The methods I suggested work for square and non-square
> (tall, not wide) matrices.
>
> lii=: 1:@%. ::0:
> lii p: i.5 3
> 1
> lii p: i.3 5
> 0
> lii i.5 3
> 0
> lii i.3 5
> 0
>
> I agree that SVP is the way to go if numerical stability
> is a concern.
>
>
>
> ----- Original Message -----
> From: John Randall <[EMAIL PROTECTED]>
> Date: Friday, September 7, 2007 9:05
> Subject: Re: [Jgeneral] linear independence?
> To: General forum <[email protected]>
>
> > Roger Hui wrote:
> > > To work with rows rather than columns, transpose
> > > the matrix, and then:
> > >
> > > Method 0: the columns are linearly independent if
> > > the matrix is invertible.
> > >
> > > lii=: 1:@%. ::0:
> > >
> > > Method 1: the columns are linearly independent
> > > if the determinant is non-zero:
> > >
> > > lid=: 0: ~: [: -/ .* (|: +/ .* ])^:(>/@$)
> >
> > I agree that this is the best way to go with square
> > matrices. The rref
> > method I suggested (which mimics pencil and paper methods) is
> a
> > good start
> > for nonsquare matrices. It can probably done better than
> > my suggested
> > code.
> >
> > However, the question of finding the rank of a matrix is difficult
> > numerically. The method usually suggested is singular value
> > decomposition, but there has been a lot of work on methods for
> special> matrices. See, for example
> >
> > <http://www.neiu.edu/~zzeng/Papers/rankrev.pdf>
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