English
There is a Frobenius-based NormedAlgebra structure on matrix algebras over a normed field, extending the Frobenius norm to scalar-mcalar interactions.
Русский
Матрицы образуют нормированную алгебру Фробениуса над нормированным полем, нормa согласуется с алгебраическими операциями.
LaTeX
$$NormedAlgebra on Matrix m m α with Frobenius norm$$
Lean4
/-- Normed algebra instance (using the Frobenius norm) for matrices over `ℝ` or `ℂ`. Not
declared as an instance because there are several natural choices for defining the norm of a
matrix. -/
@[local instance]
def frobeniusNormedAlgebra [DecidableEq m] [NormedField R] [NormedAlgebra R α] : NormedAlgebra R (Matrix m m α) :=
{ Matrix.frobeniusNormedSpace, Matrix.instAlgebra with }
