True, Every normal unitary operator u: x! x exists.
False, An if only if it is invertible, a matrix qualifies as unitary.
What is the matrix?
A group of numbers built up in a rectangular array with rows and columns. The elements, or entries, of the matrix, are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics.
Here, we have
a. Every unitary operator U:X→X is normal as an operator A is unitary if A*A = AA* = I and an operator is normal if A*A = AA*.
Hence, every unitary operator u: x → x is normal.
b. A unitary matrix is always invertible but an invertible matrix need not be unitary. An invertible matrix A is unitary if A⁻¹ = A*
Hence, it is not true.
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