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MHB Find Eigenvalues & Basis C2 Matrix: Help!
- Thread starter wefweff
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- Basis Eigenvalues Matrix
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The discussion centers on finding eigenvalues for a C2 matrix, with the key point being that the matrix does not have real eigenvalues. Instead, the eigenvalues are complex, specifically $-5 \pm i$. Participants express difficulty in understanding the problem and seek clarification on the solution process. The focus is on grasping the concept of complex eigenvalues in the context of matrix analysis. Understanding these eigenvalues is crucial for solving related mathematical problems.
Obviously, there is something elementary I am missing here.
To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix
in the real plane; taking the transpose we get
which then corresponds to a-bi...
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