I came across following matrix equations:
$(w^*)^TX^TX=y^TX \quad\quad\quad...\text{equation(1)} $
$(X^TXw^*=X^Ty) \quad\quad\quad...\text{equation(2)}$
All $X,w^*$ and $y$ and matrices or vectors. And ${x}^T$ means transpose of $x$. Then how equation(1) leads to equation(2)? Is it purely through matrix algebra or is there any calculation based on context (which I havent specified in this problem hoping it to be purely based on matrix algebra)?
It is a general rule of matrix multiplication that $$ (A\cdot B)^{\tau} = B^\tau \cdot A^\tau $$ Multiplication by a vector is matrix multiplication, too.