proposition 5.54 prop:lin-same-dim-isomorphic

open in the book · parts/02-mathematical-methods/03-linear-algebra-representations.tex:2409 · p. 125

Rests on

depends_on definition 5.15 Basis ¶
- depends_on definition 5.12 Subspace generated by a set of vectors ¶
  - depends_on definition 5.5 Linear combination ¶
    - depends_on definition 4.33 Vector space ¶
      - depends_on definition 4.8 Commutativity; abelian structure ¶
      - depends_on definition 4.32 Field ¶
      - depends_on definition 4.31 Module ¶
  - depends_on definition 5.7 Vector subspace ¶
    - depends_on definition 5.5 Linear combination ¶ ↺
  - proves proof ch:03-linear-algebra-representations@proof-3 ¶
- depends_on definition 5.14 Linear independence ¶
  - depends_on definition 5.5 Linear combination ¶ ↺
depends_on definition 5.16 Dimension ¶
- depends_on definition 5.15 Basis ¶ ↺
depends_on definition 5.53 Isomorphism ¶
- depends_on definition 5.37 Linear transformation ¶
  - depends_on definition 4.33 Vector space ¶ ↺
depends_on proposition 5.45 prop:lin-matrix-unique ¶
- depends_on definition 5.15 Basis ¶ ↺
- depends_on definition 5.37 Linear transformation ¶ ↺
- depends_on equation 5.29 eq:lin-indepli2 ¶
- depends_on equation 5.74 eq:lin-matrix-rep ¶
- proves proof ch:03-linear-algebra-representations@proof-16 ¶
proves proof ch:03-linear-algebra-representations@proof-20 ¶

Nothing declares a dependency on this node yet.

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Basis	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:2412
`depends_on`	→	Dimension	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:2412
`depends_on`	→	Isomorphism	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:2412
`depends_on`	→	prop:lin-matrix-unique	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:2412
`proves`	←	ch:03-linear-algebra-representations@proof-20	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:2418