Matrix Review (Stanford CS229)

Cost Prediction (Hypothesis result)= Data Matrix * Parameters

• House sizes:
  $$
  \begin{Bmatrix}
  2104 \\
  1416 \\
  1534 \\
  852
  \end{Bmatrix}_{4\times1}
  $$

• Hypothesis equation:
  $$h_{\theta}(x)=-40+0.25x$$

• Data Matrix:
  $$
  \begin{bmatrix}
  1 & 2104 \\
  1 & 1416 \\
  1 & 1534 \\
  1 & 852
  \end{bmatrix}_{4\times2}
  $$

• Parameters vector:
  $$
  \begin{Bmatrix}
  -40 \\
  0.25
  \end{Bmatrix}_{2\times1}
  $$

• Hypothesis equation in matrix form:
  $$
  \begin{Bmatrix}
  h_{\theta}(2104) \\
  h_{\theta}(1416) \\
  h_{\theta}(1534) \\
  h_{\theta}(852) \\
  \end{Bmatrix}_{4\times1}=
  \begin{bmatrix}
  1 & 2104 \\
  1 & 1416 \\
  1 & 1534 \\
  1 & 852
  \end{bmatrix}_{4\times2}
  \begin{Bmatrix}
  -40 \\
  0.25
  \end{Bmatrix}_{2\times1}
  $$

In programming

$\mathbf{H}_{4\times1}=\mathbf{D}_{4\times2}\mathbf{P}_{2\times1}$

for (i = 0, i < 4, i++) {
    for (j = 0, j < 2, j++) {
        H(i) += D(i,j)P(j,1);
    }
}