Matritsa va vektor me'yorlarining izchilligi
Matritsa normasi ‖ ⋅ ‖ a b (\displaystyle \|\cdot \|_(ab)) ustida K m × n (\displaystyle K^(m\times n)) chaqirdi kelishilgan normalar bilan ‖ ⋅ ‖ a (\displaystyle \|\cdot \|_(a)) ustida K n (\displaystyle K^(n)) va ‖ ⋅ ‖ b (\displaystyle \|\cdot \|_(b)) ustida K m (\displaystyle K^(m)), agar:
‖ A x ‖ b ≤ ‖ A ‖ a b ‖ x ‖ a (\displaystyle \|Ax\|_(b)\leq \|A\|_(ab)\|x\|_(a))
har qanday uchun A ∈ K m × n , x ∈ K n (\displaystyle A\in K^(m\times n),x\in K^(n)). Qurilish bo'yicha operator normasi dastlabki vektor normasiga mos keladi.
Izchil, lekin bo'ysunmaydigan matritsa normalariga misollar:
Kosmosdagi barcha normalar K m × n (\displaystyle K^(m\times n)) ekvivalentdir, ya'ni har qanday ikkita norma uchun ‖ . a (\displaystyle \|.\|_(\alfa )) va ‖ . ‖ b (\displaystyle \|.\|_(\beta )) va har qanday matritsa uchun A ∈ K m × n (\displaystyle A\K^(m\times n)) qo'shaloq tengsizlik to'g'ri.
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