## A Little Maxima Function to Find the Dimensions of a Matrix

**Update**  I didn’t find it it in documentation for quite a while, but there is a built-in Maxima function matrix_size()  in the package linearalgebra that does what this little one-liner does**

I really wanted a Maxima function that works something like MATLAB size() to easily determine the number of rows and columns for a matrix $M.$  In Maxima, length(M) gives the number of rows, and so length(transpose(M)) gives the number of columns.  I put those together in a little widget matsize() that returns the list [m,n] for an $m \times n$ matrix $M:$

matsize(A):=[length(A),length(transpose(A))];

## Extracting Matrices from the Output of eigenvectors()

In class I sometimes need to use matrices of eigenvalues and eigenvectors, but the output of eigenvectors() isn’t particularly helpful for that out of the box.

Here are two one-liners that work in the case of simple eigenvalues.  I’ll post updates as needed:

First eigU(), takes the output of eigenvectors() and returns matrix of eigenvectors:

eigU(v):=transpose(apply('matrix,makelist(part(v,2,i,1),i,1,length(part(v,2)),1)));

And eigdiag(), which takes the output of eigenvectors() and returns diagonal matrix of eigenvalues:

eigdiag(v):=apply('diag_matrix,part(v,1,1));

For a matrix with a full set of eigenvectors but eigenvalues of multiplicity greater than one, the lines above fail.  A version of the above that works correctly in that case could look like:

eigdiag(v):=apply('diag_matrix,flatten(makelist(makelist(part(v,1,1,j),i,1,part(v,1,2,j)),j,1,length(part(v,1,1)))));

eigU(v):=transpose(apply('matrix,makelist(makelist(flatten(part(v,2))[i],i,lsum(i,i,part(v,1,2))*j+1,lsum(i,i,part(v,1,2))*j+lsum(i,i,part(v,1,2))),j,0,lsum(i,i,part(v,1,2))-1)));