nLab
antilinear map

Context

Higher linear algebra

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology

Introductions

Definitions

Paths and cylinders

Homotopy groups

Basic facts

Theorems

Contents

Definition

Given VV a complex vector space, a function f:VVf \colon V \to V as antilinear or conjugate linear if

  • it respects sums of vectors: for all v 1,v 2v_1, v_2 in VV we have f(v 1+v 2)=f(v 1)+f(v 2)f(v_1 + v_2) = f(v_1) + f(v_2)

  • it preserves multiplication by complex numbers up to complex conjugation ()¯\overline{(-)}: for all cc \in \mathbb{C} and vcv \in c we have f(cv)=c¯f(v)f(c \cdot v) = \overline{c}\cdot f(v).

Last revised on November 1, 2017 at 17:39:17. See the history of this page for a list of all contributions to it.