- #1

PainterGuy

- 940

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- TL;DR Summary
- A function could be decomposed into even and odd parts but do those parts equally contribute to form the resultant vector?

Hi,

I understand how any function could be decomposed into even and odd parts assuming the function isn't a purely even or odd to start with.

It's just like saying that any vector in x-y plane could be decomposed into its x- and y-component assuming it doesn't lie parallel to x- or y-axis. Its x-component could be 'stronger' than its y-component, or vice versa. Or, both components could be equal.

It it possible to make a similar statement about even and odd parts of a function? Is it possible that even part is dominant compared to its odd part, and so on?

Thank you!

I understand how any function could be decomposed into even and odd parts assuming the function isn't a purely even or odd to start with.

It's just like saying that any vector in x-y plane could be decomposed into its x- and y-component assuming it doesn't lie parallel to x- or y-axis. Its x-component could be 'stronger' than its y-component, or vice versa. Or, both components could be equal.

It it possible to make a similar statement about even and odd parts of a function? Is it possible that even part is dominant compared to its odd part, and so on?

Thank you!

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