A:=<<9 | 3 | 6>, <4 | 6 | 1>, <1 | 1 | 7>>;

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with(linalg);

Warning, the protected names norm and trace have been redefined and unprotected

U:=gausselim(A);

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L:=transpose(gausselim(transpose(A)));

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LUdecomp(A, L='ll', R='rr');

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evalm(ll);

NiMtSSdtYXRyaXhHNiRJKnByb3RlY3RlZEdGJkkoX3N5c2xpYkc2IjYjNyU3JSIiIiIiIUYtNyUjIiIlIiIqRixGLTclI0YsRjEjRiwiIihGLA==

evalm(rr);

NiMtSSdtYXRyaXhHNiRJKnByb3RlY3RlZEdGJkkoX3N5c2xpYkc2IjYjNyU3JSIiIiQiIiFGLkYtNyVGLkYsRi03JUYuRi5GLA==

M:=<<2 | 10>, <7 | 44>>;gausselim(M);

NiMtSSdtYXRyaXhHNiRJKnByb3RlY3RlZEdGJkkoX3N5c2xpYkc2IjYjNyQ3JCIiIyIjNTckIiIhIiIq

transpose(gausselim(transpose(M)));

NiMtSSdtYXRyaXhHNiRJKnByb3RlY3RlZEdGJkkoX3N5c2xpYkc2IjYjNyQ3JCIiIyIiITckIiIoIiIq

A1 := <<1 | 2 | 3>, <4 | 5 | 6>, <7 | 8 | 9>>;

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AA := multiply(A1, transpose(A1));

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A1 := <<a | b | c | j>, <d | e | f | k>, <g | h | i | o>>;

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A1T := transpose(A1);

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AA := multiply(A1, A1T);

NiM+SSNBQUc2Ii1JJ21hdHJpeEc2JEkqcHJvdGVjdGVkR0YpSShfc3lzbGliR0YlNiM3JTclLCoqJEkiYUdGJSIiIyIiIiokSSJiR0YlRjFGMiokSSJjR0YlRjFGMiokSSJqR0YlRjFGMiwqKiZGMEYySSJkR0YlRjJGMiomRjRGMkkiZUdGJUYyRjIqJkY2RjJJImZHRiVGMkYyKiZGOEYySSJrR0YlRjJGMiwqKiZGMEYySSJnR0YlRjJGMiomRjRGMkkiaEdGJUYyRjIqJkY2RjJJImlHRiVGMkYyKiZGOEYySSJvR0YlRjJGMjclRjksKiokRjtGMUYyKiRGPUYxRjIqJEY/RjFGMiokRkFGMUYyLCoqJkY7RjJGREYyRjIqJkY9RjJGRkYyRjIqJkY/RjJGSEYyRjIqJkZBRjJGSkYyRjI3JUZCRlEsKiokRkRGMUYyKiRGRkYxRjIqJEZIRjFGMiokRkpGMUYy

eps := <eps1, eps2, eps3>;

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multiply(eps, AA);

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gausselim(AA);definite(AA, 'positive_def');B1 := <<-1 | 2 | 3 | 10>, <4 | -5 | 6 | 13>, <7 | -8 | 9 | -14>>;

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BB := multiply(B1, transpose(B1));

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definite(BB, 'positive_def');

NiNJJXRydWVHSSpwcm90ZWN0ZWRHRiQ=

diag(eigenvalues(BB));

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C:=<<2 | 3>, <-1 | 6>, <2 | 3>, <-1 | 6>>;

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CC := multiply(C, transpose(C));

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eigenvalues(CC);

NiYiIiFGIyIjISoiIzU=

eigenvectors(CC);

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evalf(Svd(CC));

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