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

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The number of rows in spin matrices and spinors is determined by the number of spin eigenstates, which correlates with the magnitude of the spin. Each row represents a distinct spin eigenstate, and higher spin particles have more orientations due to their increased spin magnitude. The relationship between spin magnitude and the number of possible orientations is fundamental to understanding particle behavior in quantum mechanics. This distinction clarifies that it is not merely the orientations that define the rows, but the eigenstates associated with the spin. Understanding this concept is crucial for grasping the complexities of quantum spin.
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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?
 
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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.
 
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