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Chapter 7: Q10E (page 383)

There exists a real 5 脳 5 matrix without any real eigenvalues.

Short Answer

Expert verified

False, that without any real eigenvalues there exists a real 5 脳 5 matrix.

Step by step solution

01

Define eigenvalue:

Eigenvalues is a special set of scale values associated with a set of line numbers in almost matrix measurements.

02

Explanation for the real 5 × 5 matrix without any real eigenvalues:

If a complex number Z is an eigenvalue of a matrix , then it is a root of det (A-位濒)which is a polynomial, so its complex conjugate zmust also be an eigenvalue of . Thus, since a 5脳5 matrix has 5 eigenvalues (counting their algebraic multiplicities), then at least one of them must be a real one

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Most popular questions from this chapter

find an eigenbasis for the given matrice and diagonalize:

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Arguing geometrically, find all eigenvectors and eigenvalues of the linear transformations in Exercises 15 through 22. In each case, find an eigenbasis if you can, and thus determine whether the given transformation is diagonalizable.

Rotation through an angle of 180掳inR2.

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