8.wxmx

/ Find the orthonormal basis of a given vector space using the Gram-Schmidt orthogonalization process. /

load("eigen")$;

x: entermatrix (3,4);

y: gramschmidt (x);

a:y[1][4];

f1:(y[1][1]^2+y[1][2]^2+y[1][3]^2+y[1][4]^2)^0.5$;

row1:y[1]/%$;

f2:(y[2][1]^2+y[2][2]^2+y[2][3]^2+y[2][4]^2)^0.5$;

row2:y[2]/%$;

f3:(y[3][1]^2+y[3][2]^2+y[3][3]^2+y[3][4]^2)^0.5$;

row3:y[3]/%$;

Orthonormal_Basis:addrow(matrix(row1),matrix(row2),matrix(row3));