> Eigenvalues are a topic in linear algebra. They're coefficients you can put in front of some matrices or vectors that change their magnitude.
Multiplying a vector or a matrix by any nonunit scalar changes its magnitude (hence scalar!! i.e. something that scales). Not all scalars are eigenvalues. So this isn't quite right
Think about it geometrically instead. A linear operator transforms a space. Geometrically the transformation can be one or more of stretching, compressing, or rotating (taking shearing to be a kind of stretching). The directions in the space which remain the same other than having been scaled by some factor are the eigenvectors of the transformation. The scaling factor of one of those such directions is its eigenvalue.
Multiplying a vector or a matrix by any nonunit scalar changes its magnitude (hence scalar!! i.e. something that scales). Not all scalars are eigenvalues. So this isn't quite right
Think about it geometrically instead. A linear operator transforms a space. Geometrically the transformation can be one or more of stretching, compressing, or rotating (taking shearing to be a kind of stretching). The directions in the space which remain the same other than having been scaled by some factor are the eigenvectors of the transformation. The scaling factor of one of those such directions is its eigenvalue.