example 2.18==============================================


proc iml;

b = sqrt(2);

A= {4 -1.4142136, -1.4142136 3};
xpx = t(A)*A;
a1 = eigvec(xpx);



print A;
print val;
print a1;
print xpx;
run;


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2.30
proc iml;

u_x= {4, 3, 2, 1};
print u_x;

u_x1= {4, 3};
u_x2 = {2,1};
A= {1 2};
B= {1 -2, 2 -1};

EAx_1= A*u_x1;
print EAx_1;

VarCov= {3 0 2 2, 0 1 1 0, 2 1 9 -2, 2 0 -2 4};

Covx1= {3 0, 0 1};

CovAx1= A*Covx1*A`;
print CovAx1;

Ebx2= B*u_x2;
print Ebx2;

Covx2= {9 -2, -2 4};

CovBx2 = B*Covx2*B`;
print CovBx2;

Covx_1x_2 = {2 2, 1 0};

CovAx1Bx2= A*Covx_1x_2*B`;
print CovAx1Bx2;


run;

============================================

2.32
proc iml;

u_x= {2,4,-1,3,0};
print u_x;

ux_1={2,4};
ux_2={-1,3,0};
A= {1 -1, 1 1};
B= {1 1 1, 1 1 -2};

VarCov= {4 -1 0.5 -0.5 0, -1 3 1 -1 0, 0.5 1 6 1 -1, -.5 -1 1 4 0, 0 0 -1 0 2};


Ex_1 = ux_1;
print Ex_1;

Eax_1 = A*ux_1;
print Eax_1;

Covx_1 = {4 -1, -1 3};
print Covx_1;

Covax_1 = A*Covx_1*A`;
print Covax_1;

Ex_2 = ux_2;
print Ex_2;

Ebx_2 = B*ux_2;
print Ebx_2;


Covx_2 = {6 1 -1, 1 4 0, -1 0 2};
print Covx_2;

Covbx_2 = B*Covx_2*B`;
print Covbx_2;

Covx_1x_2 = {0.5 -0.5 0, 1 -1 0};
print Covx_1x_2;

Covax_1bx_2 = A*Covx_1x_2*B`;
print Covax_1bx_2;

run;


===============================

=================================================

3.10

proc iml;

X= {3 1 0, 6 4 6, 4 2 2, 7 0 3, 5 3 4};
print X;

n_ROWS = nrow(x);
print n_ROWS;

colsumX = x[+, ];
print 'columns sums' colsumx;

/*obtain Xbar for each column*/

Xbar= {5, 2, 3};
print Xbar;

/*mean corrected matrix*/

/*generate ones

ones = j(5,3,1);
 print ones;

column1= x[,1] - 5;
print column1;
*/
y= {5 2 3, 5 2 3,5 2 3,5 2 3,5 2 3};
print y;

Xc= X - y;
print Xc;

/* Sample covariance matrix*/

S1= Xc`*Xc;
print s1;

S = S1/4;
print S;

/* verfy generalized matrix=0*/

detS = det(S);
print detS;

/* ahow Sa=0*/

a= {1, 1, -1};
Sa = S*a;
print Sa;
 run;

=============================================