Notation

  • I use lowercase to represent scalars and vectors.
  • I use uppercase to represent scalars and matrices.
  • Unless otherwise stated, let be and complex.
  • Unless otherwise stated, let be and complex.
  • is the -th largest singular value of .
  • is the -th largest eigenvalue of .
  • is the column vectorization of .

Vector Norms

Matrix Norms

Trace

(Cyclic Property) For properly sized matrices,