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.

  1. Leave a comment

Leave a Reply

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

WordPress.com Logo

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

Twitter picture

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

Facebook photo

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

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: