MATLAB: Find an orthogonal vector

matrixorthogonal

I have the following matrix: M = [3 18 0;-3 -2 5;-1 5 0;3 3 -9]

I need to find a vector that's orthogonal to all of the vectors in this matrix. I'm familiar with how to solve for a vector that's orthogonal to two vectors (solving for lambda and multiplying lambda by a vector), but not sure how to solve for multiple vectors. Any help is appreciated!

Best Answer

Never call a variable O. Consider how difficult it will be to find the bug one day, when you see or write a zero, instead of O. And consider that in some fonts, the difference between them is very slight.

As to the question, use null.

help null

Related Solutions

MATLAB: Null space vs eigenvectors

Hi Jeff, Since your eigenvalues are all distinct, what you have is basically correct. It's just that the eigenvector and the null vector don't have to be identical, merely proportional. Taking the first column of both Vnull and V and dividing element by element shows proportionality

>> V(:,1)./Vnull(:,1)
ans =
   0.7071 - 0.7071i
   0.7071 - 0.7071i
   0.7071 - 0.7071i

and the same is true for the other two columns.

MATLAB: A sparse matrix vector multiplication in C mex programming

Here is the bare bones C code for this. Most of the code consists of argument checking etc. The actual computation part of the code is only a few lines and is fairly trivial. It simply accumulates the individual element multiplies into the appropriate resulting element. The j for-loop loops over the columns of M, and the while loop does the individual element multiplies within each column.

/* Bare bones sparse matrix * full vector                               */
/* Produces a full vector result                                        */
/* Assumes all input elements are finite                                */
/* E.g., does not account for NaN or 0*inf etc.                         */
/* Programmer:  James Tursa                                             */
/* Includes ----------------------------------------------------------- */
#include "mex.h"
/* Gateway ------------------------------------------------------------ */
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{
    mwSize m, n, j, nrow;
    double *Mpr, *Vpr, *Cpr;
    mwIndex *Mir, *Mjc;
/* Argument checks */
    if( nlhs > 1 ) {
        mexErrMsgTxt("Too many outputs");
    }
    if( nrhs != 2 ) {
        mexErrMsgTxt("Need exactly two inputs");
    }
    if( !mxIsDouble(prhs[0]) || !mxIsSparse(prhs[0]) || mxIsComplex(prhs[0]) ) {
        mexErrMsgTxt("1st argument must be real double sparse matrix");
    }
    if( !mxIsDouble(prhs[1]) || mxIsSparse(prhs[1]) || mxIsComplex(prhs[1]) ||
        mxGetNumberOfDimensions(prhs[1])!=2 || mxGetN(prhs[1])!=1 ) {
        mexErrMsgTxt("2nd argument must be real double full column vector");
    }
    m = mxGetM(prhs[0]);
    n = mxGetN(prhs[0]);
    if( mxGetM(prhs[1])!=n ) {
        mexErrMsgTxt("Inner matrix dimensions must agree.");
    }
/* Create output */
    plhs[0] = mxCreateDoubleMatrix( m, 1, mxREAL );
/* Get data pointers */
    Mpr = mxGetPr(prhs[0]);
    Vpr = mxGetPr(prhs[1]);
    Cpr = mxGetPr(plhs[0]);
    Mir = mxGetIr(prhs[0]);
    Mjc = mxGetJc(prhs[0]);
/* Calculate result */
    for( j=0; j<n; j++ ) {
        nrow = Mjc[j+1] - Mjc[j];  /* Number of row elements for this column */
        while( nrow-- ) {
            Cpr[*Mir++] += *Mpr++ * Vpr[j];  /* Accumulate contribution of Vpr[j] */
        }
    }
}

Best Answer

Related Solutions

MATLAB: Null space vs eigenvectors

MATLAB: A sparse matrix vector multiplication in C mex programming

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