a matrix equation problem

Could you please help me to write this equation code

I have two matrix A, B. These matrices are square matrix 4*4,6*6 or etc and known. My equation is det(A-B*x^2)=0 How will I find x values

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[Walter Roberson]

Is x a scalar or a matrix?

Answer 1

[Teja Muppirala]

If B is invertible:

x = sqrt(eig(B\A))

Reason: det(A-B*x^2) = 0

implies that

det(B\A-I*x^2) = 0

If B is not invertible, this won't work.