# Why spin matrixes number of rows depends of spinn magnitude?

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• olgerm
In summary, spin-matrixes and spinors have more rows for particles with greater spin because the number of possible orientations depends on the magnitude of spin. This is determined by the number of spin eigenstates, not spin orientations.
olgerm
Gold Member
Why spin-matrixes and spinors have more rows for particles with greater spin (https://en.wikipedia.org/wiki/Spin_(physics)#Higher_spins)? As I understand every row is for 1 spin orientation, but why does number of possible orientations depend of magnitude of spin?

olgerm said:
Why spin-matrixes and spinors have more rows for particles with greater spin (https://en.wikipedia.org/wiki/Spin_(physics)#Higher_spins)? As I understand every row is for 1 spin orientation, but why does number of possible orientations depend of magnitude of spin?
These aren't defined by spin orientations, these are the defined by the number of spin eigenstates.

vanhees71

## 1. Why does the number of rows in a spin matrix depend on the spin magnitude?

The number of rows in a spin matrix depends on the spin magnitude because the spin magnitude determines the total number of possible states that can be represented by the matrix. This is because the spin magnitude is directly proportional to the number of possible spin orientations, which are represented by the rows in the matrix.

## 2. How does the spin magnitude affect the number of rows in a spin matrix?

The spin magnitude directly affects the number of rows in a spin matrix because it determines the number of possible spin orientations that can be represented. A higher spin magnitude will result in more possible spin orientations and therefore, more rows in the matrix.

## 3. Is there a mathematical relationship between the spin magnitude and the number of rows in a spin matrix?

Yes, there is a mathematical relationship between the spin magnitude and the number of rows in a spin matrix. The number of rows is equal to 2s+1, where s is the spin magnitude. This means that as the spin magnitude increases, the number of rows in the matrix also increases.

## 4. Can the number of rows in a spin matrix ever be less than the spin magnitude?

No, the number of rows in a spin matrix can never be less than the spin magnitude. This is because the spin magnitude represents the maximum number of possible spin orientations, and therefore, the minimum number of rows needed to represent all possible states is equal to the spin magnitude.

## 5. How does the number of rows in a spin matrix affect the calculations or properties of the matrix?

The number of rows in a spin matrix affects the calculations and properties of the matrix by determining the dimensionality of the matrix. This affects how the matrix can be manipulated and used in calculations, as well as the number of elements that need to be considered. A larger number of rows may also result in more complex calculations and properties.

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