Matrix inverse question

Hi,

Say I is the identity matrix, and M and K are real, symmetric positive
semi-definite (psd) matrices. All are n x n matrices, to be concrete.

Is I+MK necessarily invertible?

If MK were PSD (e.g. if M and K had t same eigenvetors), then it's
obviously true, but MK is not even symmetric in general.

Thanks,
David




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