# Vector Norm Calculator

Enter the vector components below to solve the L1, L2, and L norm.

Vector Coordinates
Vector Coordinates

## Vector Norm:

 𝓁1: 𝓁2: 𝓁∞:

### Steps to Solve

#### Solve the 𝓁1 Norm

The 𝓁1 norm is the sum of the vector component's absolute values

𝓁1 = |x| + |y| + |z|

#### Substitute Values and Solve

Enter vector coordinates above to see the solution here

#### Solve the 𝓁2 Norm

The 𝓁2 norm is the vector magnitude, use the vector magnitude formula to solve

𝓁2 = x² + y² + z²

#### Substitute Values and Solve

Enter vector coordinates above to see the solution here

#### Solve the 𝓁∞ Norm

The L norm is the max value of the absolute value of the vector components

𝓁 = max(|x|, |y|, |z|)

#### Substitute Values and Solve

Enter vector coordinates above to see the solution here

Learn how we calculated this below

## How to Find Vector Norm

In Linear Algebra, a norm is a way of expressing the total length of the vectors in a space. Commonly, the norm is referred to as the vector’s magnitude, and there are several ways to calculate the norm.

## How to Find the 𝓁1 Norm

The 𝓁1 norm is the sum of the vector’s components. This is sometimes referred to as a taxicab norm since it is equal to the path a taxi might take to get from the origin point to the vector’s coordinates.

### 𝓁1 Norm Formula

Since the 𝓁1 norm is the sum of the component’s absolute values, the formula for the 𝓁1 norm is:

𝓁1 = |x| + |y| + |z|

Thus, the 𝓁1 norm is equal to the absolute value of x plus the absolute value of y plus the absolute value of z.

## How to Find the 𝓁2 Norm

The 𝓁2 norm is sometimes referred to as the Euclidean norm, and you can find it using the vector magnitude formula.

## 𝓁2 Norm Formula

The 𝓁2 norm is equal to the square root of the sum of the squares of each component of the vector. The formula looks like this:

|a|= x² + y² + z²

Thus, the 𝓁2 norm of a vector is equal to the square root of the sum of the square of each of the vector’s components x, y, and z.

## How to Find the 𝓁∞ Norm

The 𝓁 norm is equal to the absolute value of the largest magnitude of each of the vector’s components. Thus, the 𝓁 norm is equal to the largest component value in the vector.

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