In this lecutre, we will discuss matrix transformations, which are functions that arise from multiplying a matrix by a vector. We will establish some vocabulary that we will be using when discussing these types of functions.
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T is the transformation. If x is a vector, then T(x) is the image of x. Sometimes we'll refer to the transformation as "T(x)" (where x is just a generic variable, not a specific vector). This is similar to when we refer to a function as f or f(x) interchangeably.
I wonder why mathematicians decide to use many jargons which refer to the same shit? Domain -> Codomain... is the same as ... Image -> Range.... T refers to f which is a function.... Heck....
As explained in the video, domain, codomain, image, and range all refer to different things. It is important to use precise language so that our meaning is clear. Since transformations are a special kind of function, we often (but not always) use "T" since it is the first letter of the word "transformation."
