Documentation

Mathlib.Analysis.Complex.OperatorNorm

The basic continuous linear maps associated to #

The continuous linear maps Complex.reClm (real part), Complex.imClm (imaginary part), Complex.conjCle (conjugation), and Complex.ofRealClm (inclusion of ) were introduced in Analysis.Complex.Basic. This file contains a few calculations requiring more imports: the operator norm and (for Complex.conjCle) the determinant.

@[simp]
theorem Complex.det_conjLie :
LinearMap.det Complex.conjLie.toLinearEquiv = -1

The determinant of conjLie, as a linear map.

@[simp]
theorem Complex.linearEquiv_det_conjLie :
LinearEquiv.det Complex.conjLie.toLinearEquiv = -1

The determinant of conjLie, as a linear equiv.