Det exp of block Triangular id
Matrix.det_exp_of_blockTriangular_id
Plain-language statement
Lie's trace formula for upper triangular matrices.
Exact Lean statement
lemma det_exp_of_blockTriangular_id {A : Matrix m m ๐} (hA : BlockTriangular A id) :
(NormedSpace.exp A).det = NormedSpace.exp A.traceFormal artifact
Lean source
lemma det_exp_of_blockTriangular_id {A : Matrix m m ๐} (hA : BlockTriangular A id) : (NormedSpace.exp A).det = NormedSpace.exp A.trace := by have h_exp_upper : BlockTriangular (NormedSpace.exp A) id := blockTriangular_exp_of_blockTriangular_id hA rw [det_of_upperTriangular h_exp_upper] have h_diag_exp : (NormedSpace.exp A).diag = fun i => NormedSpace.exp (A i i) := diag_exp_of_blockTriangular_id hA simp_rw [โ diag_apply] simp_rw [h_diag_exp] rw [โ NormedSpace.exp_sum Finset.univ] congr 1- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Mathematics/DataStructures/Matrix/LieTrace.lean:152-162
Reuse this declaration
Bring the exact result into your workflow
The import identifies the source module. Your project still needs the pinned package dependency shown on this page.
What this badge means
This completion status comes from the project or community source. It has not yet been represented here as an independent rebuild and axiom audit.
Continue in this project
Related declarations
Adiabatic relation log
adiabatic_relation_log
Plain-language statement
Adiabatic relation in logarithmic form: If S(Ua,Va,N) = S(Ub,Vb,N) with N fixed, then c * log (Ua/Ub) + log (Va/Vb) = 0.
Source project: Physlib
Person-level attribution pending.
Adiabatic relation Ua Ub Va Vb
adiabatic_relation_UaUbVaVb
Plain-language statement
Adiabatic relation in product form: If S(Ua,Va,N) = S(Ub,Vb,N) with N fixed, then (Ua/Ub)^c * (Va/Vb) = 1.
Source project: Physlib
Person-level attribution pending.
Deriv Within mean Energy Beta eq neg variance
CanonicalEnsemble.derivWithin_meanEnergy_Beta_eq_neg_variance
Plain-language statement
(โU/โฮฒ) = -Var(E) for finite systems.
Source project: Physlib
Person-level attribution pending.