45:
554:
179:" and similar), there exists an alternative form of terminological convention in which the term "transformation" is reserved only for bijections. When such a narrow notion of transformation is generalized to
533:
500:
425:
398:
371:
558:
574:
268:
579:
31:
278:
44:
263:
144:
303:
273:
176:
156:
140:
57:
298:
160:
100:
38:
313:
283:
148:
132:
308:
293:
224:
49:
525:
363:
465:
288:
529:
496:
490:
421:
394:
367:
228:
180:
111:
53:
415:
517:
388:
355:
17:
441:
518:
356:
568:
136:
492:
Mathematics across the Iron
Curtain: A History of the Algebraic Theory of Semigroups
240:
88:
333:
80:
67:
553:
152:
107:
76:
71:
208:
30:"Transformation (mathematics)" redirects here. For other uses, see
223:
The set of all transformations on a given base set, together with
43:
175:
for any function of a set into itself (especially in terms like "
520:
358:
390:
524:. Springer Science & Business Media. p.
516:Olexandr Ganyushkin; Volodymyr Mazorchuk (2008).
362:. Springer Science & Business Media. p.
354:Olexandr Ganyushkin; Volodymyr Mazorchuk (2008).
151:, and specific affine transformations, such as
495:. American Mathematical Society. p. 251.
8:
37:For broader coverage of this topic, see
325:
420:(2nd ed.). Springer. p. 29.
79:pattern. The four transformations are
27:Function that applies a set to itself
7:
334:"Self-Map -- from Wolfram MathWorld"
171:While it is common to use the term
466:"Types of Transformations in Math"
25:
552:
269:Data transformation (statistics)
32:Transformation (disambiguation)
1:
489:Christopher Hollings (2014).
254:+1) partial transformations.
279:Infinitesimal transformation
18:Transformation (mathematics)
598:
414:Wilkinson, Leland (2005).
387:Pierre A. Grillet (1995).
145:projective transformations
110:underpinning, that maps a
36:
29:
575:Transformation (function)
559:Transformation (function)
264:Coordinate transformation
141:geometric transformations
393:. CRC Press. p. 2.
304:Transformation semigroup
274:Geometric transformation
177:transformation semigroup
417:The Grammar of Graphics
299:Transformation geometry
167:Partial transformations
580:Functions and mappings
185:partial transformation
149:affine transformations
133:linear transformations
84:
39:Function (mathematics)
470:Basic-mathematics.com
314:Transformation matrix
284:Linear transformation
250:transformations and (
47:
561:at Wikimedia Commons
309:Transformation group
294:Rigid transformation
239:For a finite set of
225:function composition
219:Algebraic structures
106:, usually with some
131:. Examples include
446:www.mathsisfun.com
289:List of transforms
85:
557:Media related to
535:978-1-84800-281-4
502:978-1-4704-1493-1
442:"Transformations"
427:978-0-387-24544-7
400:978-0-8247-9662-4
373:978-1-84800-281-4
229:regular semigroup
181:partial functions
16:(Redirected from
587:
556:
540:
539:
523:
513:
507:
506:
486:
480:
479:
477:
476:
462:
456:
455:
453:
452:
438:
432:
431:
411:
405:
404:
384:
378:
377:
361:
351:
345:
344:
342:
340:
330:
143:, which include
130:
117:to itself, i.e.
21:
597:
596:
590:
589:
588:
586:
585:
584:
565:
564:
549:
544:
543:
536:
515:
514:
510:
503:
488:
487:
483:
474:
472:
464:
463:
459:
450:
448:
440:
439:
435:
428:
413:
412:
408:
401:
386:
385:
381:
374:
353:
352:
348:
338:
336:
332:
331:
327:
322:
260:
237:
221:
169:
118:
74:
61:
42:
35:
28:
23:
22:
15:
12:
11:
5:
595:
594:
591:
583:
582:
577:
567:
566:
563:
562:
548:
547:External links
545:
542:
541:
534:
508:
501:
481:
457:
433:
426:
406:
399:
379:
372:
346:
324:
323:
321:
318:
317:
316:
311:
306:
301:
296:
291:
286:
281:
276:
271:
266:
259:
256:
236:
233:
220:
217:
187:is a function
173:transformation
168:
165:
93:transformation
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
593:
592:
581:
578:
576:
573:
572:
570:
560:
555:
551:
550:
546:
537:
531:
527:
522:
521:
512:
509:
504:
498:
494:
493:
485:
482:
471:
467:
461:
458:
447:
443:
437:
434:
429:
423:
419:
418:
410:
407:
402:
396:
392:
391:
383:
380:
375:
369:
365:
360:
359:
350:
347:
335:
329:
326:
319:
315:
312:
310:
307:
305:
302:
300:
297:
295:
292:
290:
287:
285:
282:
280:
277:
275:
272:
270:
267:
265:
262:
261:
257:
255:
253:
249:
245:
242:
235:Combinatorics
234:
232:
230:
226:
218:
216:
214:
210:
206:
202:
199:, where both
198:
194:
190:
186:
182:
178:
174:
166:
164:
162:
158:
154:
150:
146:
142:
138:
137:vector spaces
134:
129:
125:
121:
116:
113:
109:
105:
102:
98:
94:
90:
82:
78:
73:
69:
65:
59:
55:
51:
46:
40:
33:
19:
519:
511:
491:
484:
473:. Retrieved
469:
460:
449:. Retrieved
445:
436:
416:
409:
389:
382:
357:
349:
337:. Retrieved
328:
251:
247:
246:, there are
243:
238:
222:
212:
211:of some set
204:
200:
196:
192:
188:
184:
172:
170:
161:translations
127:
123:
119:
114:
103:
96:
92:
86:
63:
241:cardinality
157:reflections
108:geometrical
89:mathematics
70:repetitive
68:rectangular
58:in SVG
50:composition
569:Categories
475:2019-12-13
451:2019-12-13
320:References
227:, forms a
64:transforms
183:, then a
153:rotations
339:March 4,
258:See also
101:function
97:self-map
54:mappings
52:of four
209:subsets
77:rhombic
75:into a
72:pattern
532:
499:
424:
397:
370:
81:linear
62:which
56:coded
99:is a
530:ISBN
497:ISBN
422:ISBN
395:ISBN
368:ISBN
341:2024
207:are
203:and
159:and
139:and
91:, a
135:of
112:set
95:or
87:In
571::
528:.
468:.
444:.
366:.
231:.
215:.
195:→
191::
163:.
155:,
147:,
126:→
122::
66:a
48:A
538:.
526:2
505:.
478:.
454:.
430:.
403:.
376:.
364:1
343:.
252:n
248:n
244:n
213:X
205:B
201:A
197:B
193:A
189:f
128:X
124:X
120:f
115:X
104:f
83:.
60:,
41:.
34:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
