Find the Norm [[2-1i],[3+0i],[1+0i]]

Problem

‖[2−i],[3+0*i],[1+0*i]‖

Solution

1. Identify the formula for the Euclidean norm (also known as the L2 norm) of a complex vector v=[(z_1),(z_2),(z_3)]T which is ∥v∥=√(,|(z_1)|2+|*(z_2)|2+|(z_3)|2)

2. Calculate the squared magnitude of each component using the formula |a+b*i|2=a2+b2

3. Compute the first component's squared magnitude: |2−i|2=2+(−1)2=4+1=5

4. Compute the second component's squared magnitude: |3+0*i|2=3+0=9

5. Compute the third component's squared magnitude: |1+0*i|2=1+0=1

6. Sum the squared magnitudes: 5 + 9 + 1 = 15$.

7. Take the square root of the sum to find the final norm.

Final Answer

‖[2−i],[3+0*i],[1+0*i]‖=√(,15)

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