let $A \in {M_{n \times m}}$ why every real symmetric matrix has at least one real eigenvalue? .
2026-04-07 03:34:11.1775532851
every symmetric matrix has at least one real eigenvalue
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your question can be answered in two parts. one symmetric matrices have real eigenvalues, and two that every matrix has at least one eigenvalue if the base field is algebraically closed. you put the two together to get your answer.