Theorems · Theorem · linear algebra
det_ne_zero_of_sum_row_lt_diag
∀ {K : Type u_1} {n : Type u_2} [inst : NormedField K] [inst_1 : Fintype n] [inst_2 : DecidableEq n] {A : Matrix n n K},
(∀ (k : n), ∑ j ∈ Finset.univ.erase k, ‖A k j‖ < ‖A k k‖) → A.det ≠ 0If A is a row strictly dominant diagonal matrix, then its determinant is nonzero.
- Defined in
- Mathlib.LinearAlgebra.Matrix.Gershgorin
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement · cited by 25,697
- Fintypestatement and proof · cited by 7,736
- Submoduleproof · cited by 7,192
- Norm.normstatement and proof · cited by 5,413
- Finset.sumstatement and proof · cited by 5,195
- Bot.botproof · cited by 4,720
- Matrixstatement and proof · cited by 4,303
- Finset.univstatement and proof · cited by 3,473
- NormedFieldstatement and proof · cited by 1,084
- sub_zeroproof · cited by 938
- Metric.closedBallproof · cited by 704
Cited by1
Results whose statement or proof uses this declaration.
- det_ne_zero_of_sum_col_lt_diagproof · cited by 1