CHAPTER 02.01: VECTORS: What is a vector?

In this segment, we will talk about how define a vector. A collection of numbers in a definite order is called a vector. So if we have n-numbers then we’ll call it, then it’ll be an n-dimensional vector then it is called an n-dimensional vector. So let’s look at an example in terms of symbol so let’s suppose somebody says “Yeah I have an A-vector, a vector A,” and what we are noting it by is by an arrow on the top some books will put the vector as a bold letter but since you cannot make the difference between bold vector, bold-case and unbold-case you don’t want to use bold and unbold in your writing things on the board or when you’re writing your homework by hand so we’re going to use arrows throughout this chapter.

So let’s suppose we have n-entries here. So we have n-entries right here and so since we are n-numbers here well call it an n-dimensional vector. And we have all these elements, all these entries are in a column so we call this to be a column vector. You can write these elements in a row also so if we are given a row so let’s suppose B is equal to b1, b2, all the way up to b sub-n minus 1, b sub n so then this is a row vector it’s a row vector because now all the elements are in a row this one is a n-dimensional vector this is also a n-dimensional vector but the difference is that this is a column vector and this is a row vector. And that’s the end of this segment.