Aerospace Engineering > GATE 2023 > Linear Algebra
Which of the following statement(s) is/are true with respect to eigenvalues and eigenvectors of a matrix?
A
The sum of the eigenvalues of a matrix equals the sum of the elements of the principal diagonal.
B
If λ is an eigenvalue of a matrix A, then 1/λ is always an eigenvalue of its transpose (AT).
C
If λ is an eigenvalue of an orthogonal matrix A, then 1/λ is also an eigenvalue of A.
D
If a matrix has n distinct eigenvalues, it also has n independent eigenvectors.

Correct : a

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eigenvalues and eigenvectors matrix properties Aerospace Engineering GATE 2023 GATE AE 2023 Q29 orthogonal matrix eigenvalues sum of eigenvalues trace distinct eigenvalues independent eigenvectors eigenvalue properties true/false

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