proposition 5.51 prop:lin-matrix-inverse

open in the book · parts/02-mathematical-methods/03-linear-algebra-representations.tex:2335 · p. 124

Rests on

depends_on equation 5.74 eq:lin-matrix-rep ¶
depends_on proposition 5.48 Existence, uniqueness, and linearity of the inverse ¶
- depends_on definition 5.47 Inverse of a linear transformation ¶
  - depends_on definition 5.37 Linear transformation ¶
    - 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 5.37 Linear transformation ¶ ↺
- proves proof ch:03-linear-algebra-representations@proof-17 ¶
depends_on proposition 5.45 prop:lin-matrix-unique ¶
- 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 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 5.37 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-19 ¶

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type	direction	node	provenance	where
`depends_on`	→	eq:lin-matrix-rep	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:2348
`depends_on`	→	Existence, uniqueness, and linearity of the inverse	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:2348
`depends_on`	→	prop:lin-matrix-unique	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:2348
`proves`	←	ch:03-linear-algebra-representations@proof-19	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:2351