Let \( A \in M_n({C}) \) be a normal matrix. Consider the following statements:
1. If all the eigenvalues of \( A \) are real, then \( A \) is Hermitian.
2. If all the eigenvalues of \( A \) have absolute value 1, then \( A \) is unitary.
Which one of the following is correct?
1. If all the eigenvalues of \( A \) are real, then \( A \) is Hermitian.
2. If all the eigenvalues of \( A \) have absolute value 1, then \( A \) is unitary.
Which one of the following is correct?
Show Hint
- Both I and II are TRUE
- I is TRUE and II is FALSE
- I is FALSE and II is TRUE
- Both I and II are FALSE
The Correct Option is A
Solution and Explanation
Top Questions on Absolute maxima and Absolute minima
In number theory, it is often important to find factors of an integer \( N \). The number \( N \) has two trivial factors, namely 1 and \( N \). Any other factor, if it exists, is called a non-trivial factor of \( N \). Naresh has plotted a graph of some constraints (linear inequations) with points \( A(0, 50) \), \( B(20, 40) \), \( C(50, 100) \), \( D(0, 200) \), and \( E(100, 0) \). This graph is constructed using three non-trivial constraints and two trivial constraints. One of the non-trivial constraints is \( x + 2y \geq 100 \).
Based on the above information, answer the following questions:
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- Semi-annually.
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