Let B be a matrix that has an eigenvalue of 9,
Find the eigenvalue of,

B^2 + 9B^-1

So based on the rules,

B^n has eigenvalue λ^n
Inverted B has an eigenvalue 1/λ
The eigenvalue of B + A is just the eigenvalues a + b that belong to their respected matrices.

My question is in regards to how the scalar affects the lambda value, I suspect the answer is,

I get 9^2 + 9(1/9) = 81 + 1 = 82 is the eigenvalue to the matrix B^2 + 9B^-1

Question

Let B be a matrix that has an eigenvalue of 9,
Find the eigenvalue of,

B^2 + 9B^-1

So based on the rules,

B^n has eigenvalue λ^n
Inverted B has an eigenvalue 1/λ
The eigenvalue of B + A is just the eigenvalues a + b that belong to their respected matrices.

My question is in regards to how the scalar affects the lambda value, I suspect the answer is,

I get 9^2 + 9(1/9) = 81 + 1 = 82 is the eigenvalue to the matrix B^2 + 9B^-1

australopithecus · Answer

Does this seem correct? I couldnt find a rule in my textbook or notes that addresses this property

australopithecus · Answer

Yes my way of calculating it is correct I just found a source online that demonstrated the property I was confused about.