# Matrix with fractions for indices?

• Shawnyboy
In summary, It is possible to have a matrix with fractions for indices, as a matrix is just a compact way of specifying actions on vectors and can contain any values. The equation provided represents a continuous operator with fractional indices, and it is possible for a diagonal matrix to have elements with indices corresponding to m values.
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

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?

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

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.

## 1. What is a matrix with fractions for indices?

A matrix with fractions for indices is a mathematical representation of a set of numbers in a rectangular arrangement. The fractions in the matrix serve as the indices or subscripts, indicating the position of each number within the matrix.

## 2. How do you represent a matrix with fractions for indices?

To represent a matrix with fractions for indices, you would use a set of parentheses containing rows and columns of numbers, with each number separated by a comma. The fractions would be written as subscripts next to each number, indicating its position within the matrix.

## 3. What is the purpose of using fractions for indices in a matrix?

Using fractions as indices in a matrix allows for more precise positioning of numbers within the matrix. It also makes it easier to perform operations on the matrix, such as addition, subtraction, and multiplication.

## 4. How do you add or subtract matrices with fractions for indices?

To add or subtract matrices with fractions for indices, you would first ensure that both matrices have the same number of rows and columns. Then, you would add or subtract the numbers in each corresponding position and keep the fractions as they are.

## 5. Can you multiply matrices with fractions for indices?

Yes, matrices with fractions for indices can be multiplied. To multiply two matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix would have the same number of rows as the first matrix and the same number of columns as the second matrix.

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