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 L^2 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=a^2+b^2

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

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

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