complex projective line
Word Rarity
Rare
Frequency: Zipf frequency 2.74 in modern English
48
Scrabble Score
21
Letters
5
Syllables
13
Unique Chars
Meaning
noun
A complex line (especially, the set of complex numbers regarded as such) endowed with a point at infinity (thus becoming a projective line); (more formally) the set of equivalence classes of ordered pairs (α, β) of complex numbers, not both zero, with respect to the equivalence relation "(α, β) ≡ (λα, λβ) for all nonzero complex λ".
Example Sentences
- "By way of an example, we consider in detail the complex projective line #92;C#92;mathbb#123;P#125;¹.[…]Thus via the function w#95;0 the complex projective line #92;C#92;mathbb#123;P#125;¹ becomes identified with the "extended complex plane" (i.e. the ordinary complex plane with an additional "point at infinity"). 2..2.1 Theorem The complex projective line #92;C#92;mathbb#123;P#125;¹ is diffeomorphic to the 2-dimensional sphere S²."
- "Finally, C is interested in the geometry of the complex projective line P¹(#92;C)."
- "Hence, C(#92;Gamma) is an uncountable union of complex projective lines."
- "As what is commonly called the Riemann sphere (after Bernhard Riemann, 1826–1866), the parabolic sphere #92;dot#123;S#125;² ̇provides a conformal model for the complex projective line #92;C#92;mathbb#123;P#125;¹."
Inflected Forms
Phrases
complex projective plane
complex projective space
projective coordinates
projective line
real projective line
Frequently Paired Words
complex projective plane
complex projective space
projective coordinates
projective line
real projective line
Synonyms
extended complex numbers
Riemann sphere