Add the random_orthogonal_matrix() function and its tests.

diff --git a/random_orthogonal_matrix.m b/random_orthogonal_matrix.m
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+++ b/random_orthogonal_matrix.m
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+function U = random_orthogonal_matrix(integerN)
+  %
+  % Generate a random orthogonal matrix.
+  %
+  % INPUT:
+  %
+  %   - ``integerN`` -- The dimension of the resulting square matrix.
+  %
+  % OUTPUT:
+  %
+  %   - ``U`` -- An orthogonal matrix of dimension integerN.
+  %
+  % REFERENCES:
+  %
+  %   1. G.W. Stewart, Efficient Generation of Random Orthogonal Matrices,
+  %      SIAM J. Numer. Analysis, 1980, pp. 403--409, Section 3.
+  %
+
+  % We begin by computing a random matrix A.
+  A = rand(integerN);
+
+  % The Q-R decomposition of A will give us an orthogonal factor of A.
+  % See the reference for why this doesn't suck.
+  [U, R] = qr(A);
+end

diff --git a/tests/random_orthogonal_matrix_tests.m b/tests/random_orthogonal_matrix_tests.m
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+++ b/tests/random_orthogonal_matrix_tests.m
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+for n = [ 1, 10, 25, 50, 100 ]
+  U = random_orthogonal_matrix(n);
+  actual = norm(U);
+  expected = 1;
+
+  msg = sprintf('random_orthogonal_matrix(%d) has norm 1', n);
+  unit_test_equals(msg, expected, actual);
+end