ABSTRACT
3901. Which mappings are linear operators on appropriate vector spaces:
x ↦ a ( a is a fixed vector ) ; https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203756454/84bc859e-388a-4821-81f7-7fb447dc7024/content/eq1108.tif"/>
x ↦ x + a ( a is a fixed vector ) ; https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203756454/84bc859e-388a-4821-81f7-7fb447dc7024/content/eq1109.tif"/>
x ↦ α x ( α is a fixed scalar ) ; https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203756454/84bc859e-388a-4821-81f7-7fb447dc7024/content/eq1110.tif"/>
x ↦ ( x , a ) b ( V is an Euclidean space, a , b bare fixed vectors); https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203756454/84bc859e-388a-4821-81f7-7fb447dc7024/content/eq1111.tif"/>
x ↦ ( x , a ) x ( V is an Euclidean space, a , is a fixed vectors ) ; https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203756454/84bc859e-388a-4821-81f7-7fb447dc7024/content/eq1112.tif"/>
f ( x ) ↦ f ( a x + b ) ( f ∈ ℝ [ x ] n ; a , b are fixed numbers ) ; https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203756454/84bc859e-388a-4821-81f7-7fb447dc7024/content/eq1113.tif"/>
f ( x ) ↦ f ( x + 1 ) − f ( x ) ( f ∈ ℝ [ x ] n ) ; https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203756454/84bc859e-388a-4821-81f7-7fb447dc7024/content/eq1114.tif"/>
f ( x ) ↦ f ( k ) ( x ) − ( f ∈ ℝ [ x ] n ) ; https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203756454/84bc859e-388a-4821-81f7-7fb447dc7024/content/eq1115.tif"/>
( x 1 , x 2 , x 3 ) ↦ ( x 1 + 2 , x 2 + 5 , x 3 ) ; https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203756454/84bc859e-388a-4821-81f7-7fb447dc7024/content/eq1116.tif"/>
( x 1 , x 2 , x 3 ) ↦ ( x 1 + 3 x 3 , x 2 3 , x 1 + x 3 ) ; https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203756454/84bc859e-388a-4821-81f7-7fb447dc7024/content/eq1117.tif"/>
( x 1 , x 2 , x 3 ) ↦ ( x 1 , x 2 , x 1 + x 2 + x 3 ) ? https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203756454/84bc859e-388a-4821-81f7-7fb447dc7024/content/eq1118.tif"/>
