Question

Is Theorem 4.45 true as stated for complex matrices? If not, can you formulate a similar theorem that is true? What is the Fredholm alternative for complex matrices?

    Is Theorem 4.45 true as stated for complex matrices? If not, can you formulate a similar theorem that is true? What is the Fredholm alternative for complex matrices?
 
Applied Linear Algebra (Undergraduate Texts in Mathematics)
Applied Linear Algebra (Undergraduate Texts in Mathematics)
Peter J. Olver,… 2nd Edition
Chapter 4, Problem 40 ↓

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45 Since the original question does not specify what Theorem 4.45 states, we will assume it refers to a common theorem in linear algebra that could be related to the Fredholm alternative. A typical theorem that might be referred to as Theorem 4.45 in some textbooks  Show more…

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Is Theorem 4.45 true as stated for complex matrices? If not, can you formulate a similar theorem that is true? What is the Fredholm alternative for complex matrices?
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