One Use For Quotients


If a function almost has some nice property, you can quotient out by that property to make that nice property true.

For example, covariance is a symmetric bilinear form on the space of random variables with finite second moments. But it can be strengthened into an inner product by modding out by difference by a constant. (Two random variables are considered the same if they differ by a constant under this equivalence relation).

This makes covariance positive-definite instead of just positive semi-definite. And now it’s an inner product.

Related Posts

Use of emphasis in speech

Generating a lot of language data with a theorem prover

"Litany Against Fear" in Present Tense

When it's time to party we will party hard

these are people who died

divine carrot

the frog

what it’s like to get nail phenolization

Why 0 to the power of 0 is 1

Lines and Points are Circles