Normalization | Introduction To Linear Algebra

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Back to Chapter Contents Prev Section | Next Section 2.5. Normalization The next operation that follows magnitude is normalization. Normalization consists of dividing every entry in a vector

by its magnitude to create a vector of length 1 known as the unit vector

(pronounced "v-hat").

For example, the vector

has magnitude

. It's unit vector is given by the following:

Figure 2-6 shows that

is made up of 6 unit vectors

. One can also easily see that normalization changes the magnitude to 1 but leaves the direction unchanged. Object could not be loaded.

Figure 2-6. Vector and its Unit Norm An important application of normalization is to rescale a vector to a particular magnitude without changing its direction. If we take the same vector