CHAPTER 02.17: VECTORS: What do you mean by rank of a set of vectors?
In this segment, we’ll talk about what do we mean by rank of a set of vectors? So, if we are given a set of n-dimensional vectors…so what that means is that we are given vectors that have n-components each in them. Then the maximum number of linearly number of independent vectors is the rank of the set of vectors. So you might be given n-vectors which are n-dimensional. All we are going to do is found out - hey out of those n-vectors what’s the maximum number out of those n-vectors which are linearly independent and that is the rank of the set of vectors. Keep in mind that the rank of set of vectors will always be less than or equal to the dimension of the vectors. So if somebody says “Hey I’m giving you n-dimensional vectors,” and whatever the number of vectors they give you of the n-dimension kind the rank of the set of vectors will always be less than or equal to the dimensional vectors; it never can be greater than the dimension of the vectors and we’ll see these things through an example. And that’s the end of this segment.