  The Clifford spectrum is a form of joint spectrum for noncommuting matrices.
This theory has been applied in photonics, condensed matter and string theory.
In applications, the Clifford spectrum can be efficiently approximated using
numerical methods, but this only is possible in low dimensional example. Here
we examine the higher-dimensional spheres that can arise from theoretical
examples. We also describe a constuctive method to generate five real symmetric
almost commuting matrices that have a $K$-theoretical obstruction to being
close to commuting matrices. For this, we look to matrix models of topological
electric circuits.
