Update LinearMaps.lean

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Pietro Monticone 2024-06-08 01:50:33 +02:00
parent 2425c09e87
commit 984e6f85d4

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@ -9,7 +9,7 @@ import Mathlib.Algebra.BigOperators.Fin
/-! /-!
# Linear maps # Linear maps
Some definitions and properites of linear, bilinear, and trilinear maps, along with homogeneous Some definitions and properties of linear, bilinear, and trilinear maps, along with homogeneous
quadratic and cubic equations. quadratic and cubic equations.
## TODO ## TODO
@ -62,7 +62,7 @@ instance instFun (V : Type) [AddCommMonoid V] [Module V] :
cases g cases g
simp_all simp_all
/-- The construction of a symmetric bilinear map from smul and map_add in the first factor, /-- The construction of a symmetric bilinear map from `smul` and `map_add` in the first factor,
and swap. -/ and swap. -/
@[simps!] @[simps!]
def mk₂ (f : V × V → ) (map_smul : ∀ a S T, f (a • S, T) = a * f (S, T)) def mk₂ (f : V × V → ) (map_smul : ∀ a S T, f (a • S, T) = a * f (S, T))
@ -196,7 +196,7 @@ instance instFun : FunLike (TriLinearSymm V) V (V →ₗ[] V →ₗ[]
cases g cases g
simp_all simp_all
/-- The construction of a symmetric trilinear map from smul and map_add in the first factor, /-- The construction of a symmetric trilinear map from `smul` and `map_add` in the first factor,
and two swap. -/ and two swap. -/
@[simps!] @[simps!]
def mk₃ (f : V × V × V→ ) (map_smul : ∀ a S T L, f (a • S, T, L) = a * f (S, T, L)) def mk₃ (f : V × V × V→ ) (map_smul : ∀ a S T L, f (a • S, T, L) = a * f (S, T, L))