This is a subject I struggled with the first time I took it. Ironically, this was the engineering version of it. It wasn't until I took the rigorous, axiomatic version that everything clicked.

If \(A\) is a \(3\times 3\) matrix then we can apply a linear transformation to each rgb vector via matrix multiplication, where \([r,g,b]\) are the original values ...

Representation theory was initially dismissed. Today, it’s central to much of mathematics. When representation theory emerged in the late 19th century, many mathematicians questioned its worth. In ...