What exactly do eigenvalue and eigenvector indicate?
I mean what is the importance in calculating them. We all know how to calculate them but I do not know the exact importance
What exactly do eigenvalue and eigenvector indicate?
I mean what is the importance in calculating them. We all know how to calculate them but I do not know the exact importance
Think of a matrix as an operator - one that operates on vectors, and returns another vector, which is a rotated, skewed and stretched copy of the original. Now, if we ignore length changes, some of the vectors will be left unchanged by this matrix, and retain their overall direction (though not their length): It is these vectors we call the eigenvectors of the matrix, and the factor by which their magnitude changes is called their eigenvalue.