Hello Forum,(adsbygoogle = window.adsbygoogle || []).push({});

When we represent a vector X using an orthonormal basis, we express X as a linear combination of the basis vectors:

x= a1 v1 + a2 v2 + a3 v3+ .....

Each coefficient a_i is the dot product between x and each basis vector v_i.

If the vector x is not a row (or column vector), but an array (like an image) the equation is still the same: the a_i are single numbers, while the basis vectors v_i become arrays. The array x becomes the weighted sum of multiple basis arrays.

But how does the dot product between two matrices, x and v1 for example, both of size NxN, give asingle number, the coefficient a1? The dimension does not seem to allow this matrix product to output a 1x1 vector (the single coefficient), does it?

a1=<x^T, v1>= dot product between the transpose of x and array v1....

thanks

fisico30

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Dot product between arrays: basis representation of an image

Loading...

Similar Threads - product between arrays | Date |
---|---|

A Difference Between Outer and Tensor | Feb 26, 2017 |

I Difference between direct sum and direct product | Jun 11, 2016 |

Cross product between unit vectos | Jan 14, 2014 |

Difference between tensor product and direct product? | Jun 25, 2013 |

Question on inner products between functions | Nov 28, 2012 |

**Physics Forums - The Fusion of Science and Community**