Linear algebra (and most calculus) didn&#x27;t really click for me until I needed to apply it to physics problems.<p>The general idea started to make sense in mechanics class when I could see matrices are convenient shorthand for solving multiple variables at once, and which behave like &#x27;regular&#x27; variables when trying to manipulate them algebraically.<p>Eigenvalues and eigenvectors didn&#x27;t make sense until quantum mechanics, where your &#x27;operator&#x27; is effectively a matrix and your &#x27;state&#x27; is a vector. The allowed observed values are the eigenvalues, and your final state after measurement is the corresponding eigenvector. Wave functions are then an extension of this from discrete space (useful for modelling spins for instance) to the continuum of position space.