If the matrix M - 0I in equation 4.15 has an inverse then we could multiply both sides of the equation by the inverse matrix:
-0 f0,1 Jf« b)f R) = (0)( a bJ s1,2 -0 Jf c dJl FJ 10Jl c dJ M - 0I Inverse vt Inverse of M - 0I of M - 0I
Multiplying the square matrix M - 0I by its inverse on the left-hand side would give the identity matrix, I (by definition), whereas the right-hand side would reduce to 0:
This is unhelpful as we are left with the trivial solution that R and F are equal to 0. To overcome this problem we need to assume that the matrix M - 0I does not have an inverse. This is true if the determinant of the matrix is equal to 0. This assumption can then be used to find a value for 0:
The determinant in equation 4.16 is referred to as the characteristic determinant. The whole equation 4.16 is called the characteristic equation. We can now evaluate the characteristic determinant and therefore solve the characteristic equation:
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