In the previous post we covered eigensystems of two by two matrices, being the set of unit eigenvectors v_{i} and eigenvalues λ_{i} that satisfy the relation
M × v_{i} = λ_{i} × v_{i}
To find the eigenvalues of a matrix M we solved the characteristic equation
|M - λ_{i} × I| = 0
Now for a two by two matrix this was a simple quadratic equation that we could solve with the equation we learnt in school. For larger matrices the characteristic equation is much harder to solve and we shall have to take an entirely different approach.
M × v_{i} = λ_{i} × v_{i}
To find the eigenvalues of a matrix M we solved the characteristic equation
|M - λ_{i} × I| = 0
Now for a two by two matrix this was a simple quadratic equation that we could solve with the equation we learnt in school. For larger matrices the characteristic equation is much harder to solve and we shall have to take an entirely different approach.
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