Le sujet TpSyst_Lin

A , n ×m
A=
1234
2341
3412
4123
.
A
for i = 1 : 4, for j = 1 : 4, s =i+j−1; A(i, j) = i+j−1; if (A(i, j)>4), A(i, j) = A(i, j)−4; end, end, end
M n ×m , v =size(M)v= [n, m].
B=M0M .
1≤i≤n1≤j≤m , u =M(i, :) ieme M ,
w=M(:, j)jeme M .
c=M(i, j)Mij .
v0 = linspace(0.5,1.7,6) size(v0) = [1,6] v00
size(v00) = [6,1]
v1 = 0.5 : (1.7−0.5)/5 : 1.7
a size(a) = [1,1] a∗M M/a a 6= 0
M .
N M , M +N M −N M .
N m ×k , M ∗N n ×k
A n , d =det(A)
B=inv(A)
E=M(i1 : i2, j1 : j2) M , (i2−i1+1)×(j2−j1+1) :
E= (Mij )i1≤i≤i2
j1≤j≤j2
.
M n ×m N n ×k ,
T= [M;N]n×(m+k).
Q k ×m ,
Z= [MQ] (n+k)×m .
M n ×m y n x =M\y
m , y =M∗x
zeros(n, m) ; ones(n, m) ; eye(n) ; eye(n, m) ; hilb(n) ; vander(v) ; toeplitz(v), invhilb(n)
n m v
A=hilb(n)Aij = 1/(i+j−1)
invhilb(n).
S=toeplitz(v)S v(1) ,
S(i, j) = v(abs(j−i) + 1) : M M(i, j)
j−i

M=diag(v)
v=diag(A)A .
function testeLU(A)
A
A= (Aij )1≤i,j≤n
∀k , 1≤k < n , det ((Aij )1≤i,j≤k)6= 0 .
n det ((Aij )1≤i,j≤k), k = 1, . . . , n .
function matrice(n)
A n , (2 ≤n≤5) ,
function x =sysu(U, v)
U.x =v U
function x =sysl(L, v)
L.x =v L
lu
function [L, U] = mylu(A)
A .
function y =mydet(A)
function x =sys(A, v)
A.x =v
function [P, L, U] = myplu(A)
A .