Given that the eigenvalues of matrix A of order 3 are 1,2,3, try to find the eigenvalues of B = 1 / 2A * + 3E

Do you want B = 1 / (2a *) + 3E or B = (1 / 2) a * + 3E?
This problem can be solved according to the properties of adjoint matrix, a * = |a|a's inverse, and then according to the relationship between determinant and matrix eigenvalue, the value of |a | is 6, and the eigenvalues of a's inverse can be obtained from the eigenvalues of a, which are 1, 1 / 2, 1 / 3 respectively. Finally, the original formula can be brought in
The eigenvalues of the previous formula are 37 / 12, 19 / 6 and 13 / 4
The eigenvalues of the latter formula are 6,9 / 2,4

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