Why use a matrix?
A matrix is best used to visualize any two dimensional set of numbers, colors, intensities, sized dots or other glyphs. A common form the visualization can take is the half matrix. Similar to the purpose of a regular numeric matrix, a half matrix is intended to visualize two dimensional data sets. However, unlike the whole matrix, a half matrix only displays half the field, as the other half is mirrored diagonally.
Examples
Whole Matrix vs. Half Matrix
Interactive Matrix Visualization
Positives: Clean, adequate spacing
Negatives: Lower x-axis not clearly labeled, no title
Matrix Visualization (could be better communicated using a half matrix, as the image is the same when reflected across its diagonal)
Positives: Numeric data is communicated clearly
Negatives: No indication of what numeric data is representative of, no unit of measurement for "value," no title, too little spacing between text on x-axis and y-axis, could function as a half matrix
Half Matrix Visualization
Positives: Half matrix made from whole matrix
Negatives: No title, no indication of what varying circle size represents, no key indicating what abbreviated axis labels mean, distracting text size and color
(Whole matrix below)