We’ve talked about changing bases from the standard basis to an alternate basis, and vice versa. Now we want to talk about a specific kind of basis, called an orthonormal basis, in which every vector in the basis is both 1 unit in length and orthogonal to each of the other basis vectors.
Read MoreIn other words, up to now, plotting points has always been done using the standard basis vectors i and j, or i, j, and k in three dimensions. Even when we were originally learning to plot (3,4) back in an introductory Algebra class, and we knew nothing about vectors, we were really learning to plot 3i+4j in terms of the standard basis vectors, we just didn’t know it yet. In this lesson, we want to see what it looks like to define points using different basis vectors. In other words, instead of using i=(1,0) and j=(0,1), can we use different vectors as the basis instead?
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