instContinuousAddMatrix — Mathlib

English

Matrix addition is a continuous operation: the map (A,B) ↦ A + B from M_{m×n}(R) × M_{m×n}(R) to M_{m×n}(R) is continuous.

Русский

Сложение матриц непрерывно: карта (A,B) ↦ A + B из M_{m×n}(R) × M_{m×n}(R) в M_{m×n}(R) непрерывна.

LaTeX

$$$\\operatorname{Continuous}\\big(\\lambda (A,B) : \\mathrm{M}_{m\\times n}(R) \\times \\mathrm{M}_{m\\times n}(R) \\to \\mathrm{M}_{m\\times n}(R),\\ (A,B) \\mapsto A+B\\big).$$$

Lean4

instance [Add R] [ContinuousAdd R] : ContinuousAdd (Matrix m n R) :=
  Pi.continuousAdd

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