Vector Magnitude

Implement a function to compute the magnitude (also known as the Euclidean norm) of a given vector. The magnitude of a vector is a fundamental concept in linear algebra and vector calculus, as it represents the "length" or "size" of the vector.

The magnitude of a vector $\mathbf{v} = [v_1, v_2,..., v_n]$ can be calculated using the formula $||\mathbf{v}|| = \sqrt{v_1^2 + v_2^2 +... + v_n^2}$ . To calculate this, follow these steps:

Square each component of the vector.
Sum the squared components.
Take the square root of the sum.

||\mathbf{v}|| = \sqrt{\sum_{i=1}^{n} v_i^2}

This technique is widely used in computer vision for image and signal processing.

Example:

Input:

magnitude([3, 4])

Output:

5.0000

Reasoning:

Step-by-step calculation using the Euclidean norm formula:

$\|\mathbf{v}\| = \sqrt{\sum_{i=1}^{n} v_i^2}$

Square each element:
- $3^2 = 9$
- $4^2 = 16$
Sum the squared values: $9 + 16 = 25$
Take the square root: $\sqrt{25} = 5$
Result: $5.0000$

This is the classic 3-4-5 right triangle! The magnitude represents the length of the vector from origin to point $(3,4)$ .

Constraints:

Vector length n where 1 ≤ n ≤ 1000
Vector elements are floating-point numbers
Return the result rounded to 4 decimal places

Example:

Constraints:

Test Results