Vectorized form Derivation of Multiple Linear Regression Cost Function

Question

Can some one with expertise explain how the following vectorized format of multiple linear regression is derived from given independent variable matrix with intercept X and dependent variable matrix Y, with m rows and n columns with n theta parameters? In Andrew Ng class, I am bit lost here on how this and non vectorized cost function are same?

Answer 1

Ah! I think I got the answer. I forgot that what is happening is a square of a vector in the error part of the function. Hence it is transpose of vector.vector. Still not able to understand how X is defined with transposes of all independent variables in above definition, as I believe it is a matrix of dependent variables including intercept.