The magnitude or size of a vector v in real vector space is gauged by its norm, typically symbolized as ||v||. The most frequently applied norms encompass the Euclidean norm (also recognized as the 2-norm) and the absolute value norm for single-dimension vectors. For a norm to be valid, it should adhere to specific properties such as positivity, scalability, and the triangle inequality.
| Topic | Problem | Solution |
|---|---|---|
| None | Find the norm of the vector \( v = [3, -4, 12] \)… | The norm of a vector \( v \) in real vector space is given by the square root of the sum of the squ… |