This is a brief summary of ML course provided by Andrew Ng and Stanford in Coursera.
You can find the lecture video and additional materials in
https://www.coursera.org/learn/machine-learning/home/welcome
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To solve for the params $\theta_0$ and $\theta_1$ all in one shot, without needing an iterative algorithm like gradient descent.
Matrix-multiplication is one of the key steps that you need to know.
$\left[\begin{array} {rrr} 1 & 3 & 2 \\ 4 & 0 & 1 \end{array}\right] $ $\left[\begin{array} {rrr} 1 & 3 \\ 0 & 1 \\ 5 & 2 \end{array}\right] $ = $\left[\begin{array} {rrr} 11 & 10 \\ 9 & 14 \end{array}\right] $
$\left[\begin{array} {rrr} 1 & 3 & 2 \\ 4 & 0 & 1 \end{array}\right] $ $\left[\begin{array} {rrr} 1 \\ 0 \\ 5 \end{array}\right] $ = $\left[\begin{array} {rrr} 11 \\ 9 \end{array}\right] $
$\left[\begin{array} {rrr} 1 & 3 & 2 \\ 4 & 0 & 1 \end{array}\right] $ $\left[\begin{array} {rrr} 3 \\ 1 \\ 2 \end{array}\right] $ = $\left[\begin{array} {rrr} 10 \\ 14 \end{array}\right] $
Take this two vectors' elements and plugging them together.
Works only if m x n , n x o (where n matches) to output m x o matrix.
Example:
$\left[\begin{array} {rrr} 1 & 3 \\ 2 & 5 \end{array}\right] $ $\left[\begin{array} {rrr}0 & 1 \\ 3 & 2 \end{array}\right] $ = $\left[\begin{array} {rrr} 9 & 7 \\ 15 & 12 \end{array}\right] $
$\left[\begin{array} {rrr} 1 & 3 \\ 2 & 5 \end{array}\right] $ $\left[\begin{array} {rrr}0 \\ 3 \end{array}\right] $ = $\left[\begin{array} {rrr} 9 \\ 15 \end{array}\right] $
$\left[\begin{array} {rrr} 1 & 3 \\ 2 & 5 \end{array}\right] $ $\left[\begin{array} {rrr}1 \\ 2 \end{array}\right] $ = $\left[\begin{array} {rrr} 7 \\ 12 \end{array}\right] $
Quiz: In the equation $\left[\begin{array} {rrr} 1 & 3 \\ 2 & 4 \\ 0 & 5 \end{array}\right] $ $\left[\begin{array} {rrr} 1 & 0 \\ 2 & 3 \end{array}\right] $ = $\left[\begin{array} {rrr} 7 & 9 \\ a & b \\ c & d \end{array}\right] $ what is a,b,c,d?
Answer: 10, 12, 10, 15
Lecturer's Note
We multiply two matrices by breaking it into several vector multiplications and concatenating the result.
$\left[\begin{array} {rrr} a & b \\ c & d \\ e & f \end{array}\right] $ $\left[\begin{array} {rrr}w & x \\ y & z \end{array}\right] $ = $\left[\begin{array} {rrr} aw+by & ax + bz \\ cw + dy & cx + dz \\ ew + fy & ex + fz \end{array}\right] $
An m x n matrix multiplied by an n x o matrix results in an m x o matrix. In the above example, a 3 x 2 matrix times a 2 x 2 matrix resulted in a 3 x 2 matrix.
To multiply two matrices, the number of columns of the first matrix must equal the number of rows of the second matrix.
