Why introduce matrix in quantum mechanics

Because it helps solve problems.

 

Its a natural part of a vector space's structure and associated linear transformations as any book on linear algebra will attest to. Same in QM, since its underlying space of states forms a vector space.

Thanks
Bill

 

A matrix is a way to transform a vector into another vector. For example, it can rotate a vector. In QM a state vector is used to represent Quantum State so if you want to operate on that state (measure spin for example) you can use a particular type of matrix (an observable such as a spin operator) to operate on the spin state vector. Using this you can determine the measured state, and probabilities.