Word Pronunciation & Dictionary

dual space

Word Rarity Uncommon

Frequency: Zipf frequency 4.23 in modern English

Syllables: du-al s-pace
IPA

14

Scrabble Score

9

Letters

3

Syllables

8

Unique Chars

Meaning

noun

The vector space which comprises the set of linear functionals of a given vector space.

noun

The vector space which comprises the set of continuous linear functionals of a given topological vector space.

Example Sentences

"The dual space of a Banach space X is the vector space of continuous linear functions X#92;rightarrow#92;mathbb#123;R#125;, which are called functionals. Similar notation is used for duality pairing between the Banach space X and its dual space X': #92;left#92;langleu,v#92;right#92;rangle is the result of applying the functional u#92;inX' to v#92;inX: #92;left#92;langleu,v#92;right#92;rangle#61;u(v) explicitly uses the fact that u is a function X#92;rightarrow#92;mathbb#123;R#125;."

Inflected Forms

dual spaces (plural)

Synonyms

algebraic dual space dual vector space continuous dual space continuous dual

Questions

What does dual space mean?: The vector space which comprises the set of linear functionals of a given vector space.

How to pronounce dual space

Open the pronunciation page — Open the Speakur entry for “dual space”.
Read the phonetic spelling — Read the IPA spelling () so you know which sounds to aim for.
Play the audio — Click Play to hear reference audio for “dual space”.
Repeat and practice — Say “dual space” aloud, matching stress and vowels until it feels natural.