The three musketeers

Given vectors $\mathbf{x}$ and $\mathbf{y}$ , the three quantities $\mathbf{x}\cdot\mathbf{x}$ , $\mathbf{x}\cdot\mathbf{y}$ and $\mathbf{y}\cdot\mathbf{y}$ are very interesting indeed.

In fact, the concept of inner product vector space revolves largely around those quantities. The underlying mathematical fact is the Cauchy-Schwarz inequality $(\mathbf{x}\cdot\mathbf{y})^2 \le (\mathbf{x}\cdot\mathbf{x})\times (\mathbf{y}\cdot\mathbf{y})$ , which is a corollary of the axioms of an inner product vector space.

Like this:

Be the first to like this post.

This entry was posted on October 29, 2010, 8:49 pm and is filed under mathematics. You can follow any responses to this entry through RSS 2.0. You can leave a response, or trackback from your own site.

Leave a Reply Cancel reply

Enter your comment here...

Fill in your details below or click an icon to log in:

Email (required) (Address never made public)

Name (required)

Website

You are commenting using your WordPress.com account. ( Log Out / Change )

You are commenting using your Twitter account. ( Log Out / Change )

You are commenting using your Facebook account. ( Log Out / Change )

Cancel

Connecting to %s

On Another Dimension