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.
QUYIDAGI MASALADA C++ DASTURLASH tlida codi yozilgan
Namunaviy masala Tezkor tartiblash usuli yordamida n ta (n>0) butun sonlardan iborat x massiv kamaymaydigan ko‘rinishda tartiblansin.
void T e z k o rT artiblasWint *a, int i_chap, int iu n g l
{
int chap, ung, ai;
if (i_chap> - iung) return;
chap-i_chap;
ung-i_ung;
ai-a[(chap+ungM2);
while{chap<-ung)
{
while(a[chap]while(a[ung}>ai) ung-;
if(chap<—ung)
{
int vaqtincha-a[chapl;
a[chap]-a[unfll;
alungl-vaqtincha;
chap++; ung-;
}
}
Tezkor_Tartiblash(a, i_chap, ung);
Tezkor_Tartiblash(ar chap, ijmg);
}
int main()
{
int *x;
int n;
c in » n ;
x -n e w int [n];
for (inti-0;icout«"Berilgan massiv”« e n d l;
forfint i-0;icout«endl;
Tezkor_Tartiblash(x,0,n-1);
coutcc'Tartibiangan massiv:"«endl;
forlint i-0 ;i< n ;i+ +) c o u t « x [i] «'\t';
return 0;
XULOSA
Qilingan ishdan xulosam shuki Matritsaning faqat uchta normasi mavjud ekan
