# Matrix with fractions for indices?

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1. May 20, 2015

### Shawnyboy

Hi PF Peeps!

Something came up while I was studying for my QM1 class. Basically we want to represent operators as matrices and in one case the matrix element is defined by the formula :

$<m'|m> = \frac{h}{2\pi}\sqrt{\frac{15}{4} - m(m+1)} \delta_{m',m+1}$

But the thing is we know m takes on the fractional values -3/2, -1/2, 1/2, 3/2. So basically my question is simply put: can you have a matrix with fractions for indeces?

Thanks,
Shawn

2. May 20, 2015

### sk1105

Yes you can. A matrix is essentially just a compact way of specifying what action to perform on each component of a vector to make another vector, and can contain whatever you want. Is there something you've seen or heard that made you think fractional indices weren't possible?

3. May 22, 2015

### jk22

Maybe it is because your matrix represents a continuous operator hence having continuous indices ?

4. May 23, 2015

### theodoros.mihos

I think your equation is not complete. If this is an eigenvalues equation then the diagonal matrix must have elements like:
$$\sqrt{\frac{15}{4}-i(i+1)}$$where i the correspond to matrix column/row element by the same index on m values.