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. |