Thread: Problem 1.3 c
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Old 06-10-2016, 03:19 AM
henry2015 henry2015 is offline
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Join Date: Aug 2015
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Default Re: Problem 1.3 c

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.

Last edited by henry2015; 06-10-2016 at 03:38 AM. Reason: syntax error
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