Chapter Five

Consider the Lowly 2 × 2 Matrix

March 1996


If you're into computer graphics you gotta love matrices. But sometimes matrices are so … complicated. They have determinants, eigenvalues, and singular value decompositions. What does all this stuff really mean? What does it mean, for example, to take the square root of a matrix? How about the logarithm of a matrix?

I have built up my intuition about matrices by playing extensively with the simplest form, the lowly 2×2 matrix. These almost look too simple to be interesting, but they show off many of the properties of larger matrices. Better yet, we can write out explicit formulas for quantities ...

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