where $U$ and $V^T$ are square and $\Sigma$ is the same size as $A$. $\Sigma$ is a diagonal matrix and contains the[singular values](https://en.wikipedia.org/wiki/Singular_value) of $A$, organized from largest to smallest. These values are always non-negative and can be used as an indicator of the "importance" of some features represented by the matrix $A$.

Let's see how this works in practice with just one matrix first. Note that according to[colorimetry](https://en.wikipedia.org/wiki/Grayscale#Colorimetric_(perceptual_luminance-reserving)_conversion_to_grayscale),

Let's see how this works in practice with just one matrix first. Note that according to[colorimetry](https://en.wikipedia.org/wiki/Grayscale#Colorimetric_(perceptual_luminance-preserving)_conversion_to_grayscale),

it is possible to obtain a fairly reasonable grayscale version of our color image if we apply the formula