proposition 5.67 Adjointness of pullback and pushforward
open in the book ·
parts/02-mathematical-methods/03-linear-algebra-representations.tex:2982
· p. 132
Rests on
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depends_on
definition 5.59
Dual space
¶
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depends_on
definition 5.46
Functional
¶
-
depends_on
definition 5.37
Linear transformation
¶
- depends_on definition 4.33 Vector space ¶
-
depends_on
definition 5.37
Linear transformation
¶
-
depends_on
definition 5.46
Functional
¶
-
depends_on
definition 5.66
Pushforward
¶
- depends_on definition 5.59 Dual space ¶ ↺
- depends_on definition 5.37 Linear transformation ¶ ↺
- depends_on notation 5.65 The dual pairing ¶
- proves proof ch:03-linear-algebra-representations@proof-24 ¶
Supports
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Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
depends_on |
→ | Dual space | declared | parts/02-mathematical-methods/03-linear-algebra-representations.tex:3009 |
depends_on |
→ | Pushforward | declared | parts/02-mathematical-methods/03-linear-algebra-representations.tex:3009 |
depends_on |
→ | The dual pairing | declared | parts/02-mathematical-methods/03-linear-algebra-representations.tex:3009 |
proves |
← | ch:03-linear-algebra-representations@proof-24 | declared | parts/02-mathematical-methods/03-linear-algebra-representations.tex:3012 |