is the statement: "A symmetric matrix has a real eigenvalues" obvious??
the textbook assumes a direct link, but nowhere in textbook is a proof of the latter statement
HELP~!
Theorem 8.8.7 (not covered in this semester).
"If A is a real symmetric matrix, then A has real eigenvalues."
When A is a complex symmetric, (counterexample)
1 i
i 1
has eigenvalues 1+i, 1-i, and they are not real.
More advanced theorems can be found in section 8.9 or another advanced course.
Theorem 8.8.7 (not covered in this semester).
"If A is a real symmetric matrix, then A has real eigenvalues."
When A is a complex symmetric, (counterexample)
1 i
i 1
has eigenvalues 1+i, 1-i, and they are not real.
More advanced theorems can be found in section 8.9 or another advanced course.