• I don't even know what the correct name for what I want to study, but I essentially want to learn more about matrices
• If you have a matrix that is unitary, then its matrix inverse is equal to its conjugate transpose
• Why are these properties useful? Well you get a bunch of properties. One of them including an orthonormal (perpendicular) basis, which makes linear transformations really easy.
• If you have a matrix that is hermitian, then its conjugate transpose is equal to itself
• Hermitian matrices can be diagonalized and eigendecomposed.