## Characteristic equation formula for a nxn matrix ?

So I know that the characteristic equation for a 2x2 matrix can be given by

$$t^2 - traceA + |A|$$

So how would this be generalised for a 4x4 or higher matrix ?

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 Blog Entries: 1 Recognitions: Homework Help You forgot some t's in your equation but it's clear what you are referring to. The characteristic equation is a polynomial whose roots are the eigenvalues of the matrix. So if we have $$(x-\lambda_1)\times....\times (x-\lambda_n) = a_n x^n + a_{n-1}x^{n-1}.... + a_1x + a_0$$ then an-1 is the sum of the negatives of the eigenvalues, so an-1 is the negative trace. a0 is the product of the eigenvalues with minus signs, so a0 is plus or minus the determinant of the matrix (depending on whether n is even or odd). The other ones are constructed by adding up multiples of the eigenvalues, for example [tex] a_{n-2} = \sum_{i