. Show that LDA using <span class="arithmatex">\(\boldsymbol{\hat Y}\)</span> is identical to LDA in the original space.</p>
</details>
<details class="done"><summary>Soln. 4.3</summary><p>We start by introducing notations used in Chapter 3.</p>
<p>Let <span class="arithmatex">\(x_i^T = (x_{i1}, ..., x_{ip})\in \mathbb{R}^{1\times p}\)</span>, <span class="arithmatex">\(\bb{1}^T = (1,...,1)\in \mathbb{R}^{1\times p}\)</span>, <span class="arithmatex">\(Y^T = (y_1, ..., y_N)\in \mathbb{R}^{1\times N}\)</span