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henry2015 · #3 06-10-2016, 03:19 AM

Hi,

I just revisited this problem again.

If I substitute w(t-1) with
$\begin{bmatrix}w{_0}\\w{_1}\\w{_2}\end{bmatrix}$

x(t-1) with
$\begin{bmatrix}1\\x{_1}\\x{_2}\end{bmatrix}$

I could get
$||w(t)||{^2}$
$= ||w(t-1) + y(t-1)x(t-1)||{^2}$
$= ||w(t-1)||{^2} + y(t-1){^2}||x(t-1)||{^2} + 2y(t-1)w{^T}(t-1)x(t-1)$

and then use the hint to get the answer.

However, the dimension of x and w can be more than 3. I just wonder whether there is a more generic proof.

Thanks in advance.