File:ComplexLinearMapping.svg
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Size of this PNG preview of this SVG file: 638 × 312 pixels. Other resolutions: 320 × 156 pixels | 640 × 313 pixels | 1,024 × 501 pixels | 1,280 × 626 pixels | 2,560 × 1,252 pixels.
Original file (SVG file, nominally 638 × 312 pixels, file size: 30 KB)
Captions
Captions
Complex linear mapping
Summary[edit]
| Description |
Dansk: Illustration af den komplekse lineære funktion f(z) = a + b*i, hvor a = sqrt(3) + i og b = 2 + i.
Et net af enhedskvadrater i z-planet afbildes ved f i et andet kvadratisk net i w-planet. De tre komplekse tal 0, 1 og i samt afbildningens fikspunkt z* er i z-planet markeret med farvede prikker hhv. et sort kryds. Deres billeder i w-planet har de samme signaturer. Fikspunktet er defineret ved, at f(z*) = z*, så det bliver som det eneste liggende samme sted.English: Illustration of the complex linear function f(z) = a + b*i, where a = sqrt(3) + i og b = 2 + i.
A mesh of unit squares in the z-plane are mapped by f onto another square net in the w-planet. In the z-plane the three complex numbers 0, 1 and i as well as the fixed point z* of the mapping are marked by colored dots and a black cross, respectively. Their images in the w-plane have the same signatures. The fixed point is defined by the requirement f(z*) = z*, so as the only number it retains its position. |
| Date | |
| Source | Own work |
| Author | AstroOgier |
Licensing[edit]
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 14:29, 15 October 2019 | | 638 × 312 (30 KB) | AstroOgier (talk | contribs) | User created page with UploadWizard |
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