pu'e'ei

valsi

pu'e'ei

type

experimental cmavo

creator

krtisfranks

time entered

Mon Jan 9 09:02:38 2023  

English

Definition #73114 - Preferred

 

selma'o

VUhU3

definition

mekso binary operator: generate span; outputs span MATH

$(X_1, X_2)=$

(X₁, X₂) = span MATH

$_{X_2}(X_1)$

_X2(X₁); set of all (finite) sums of terms of form cv, where v is an element of algebraic structure X₁ (wherein scalar multiplication and summation is defined), and c is a scalar belonging to ring X₂.

notes

For example, the span of vectors v₁ and v₂ in vector space V over the field of exactly all real numbers R has X₁ = Intersect(V, Set MATH

$(v_1, v_2))$

(v₁, v₂)) and X₂ = R and yields output Set MATH

$(c_1 v_1 + c_2 v_2 : c_i$

(c₁v₁ + c₂v₂ : c_i in R for alli), where scalar multiplication and vector addition are as defined in V.

gloss words

• linear combination
• linear superposition
• span ; algebra

created by

krtisfranks

vote information

1

time

Mon Jan 9 09:08:49 2023

Examples

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