diff --git a/lapack/testlapack/dlanv2.go b/lapack/testlapack/dlanv2.go
index 8d69f0b2..98403a5c 100644
--- a/lapack/testlapack/dlanv2.go
+++ b/lapack/testlapack/dlanv2.go
@@ -61,17 +61,24 @@ func dlanv2Test(t *testing.T, impl Dlanv2er, a, b, c, d float64) {
 
 	mat := fmt.Sprintf("[%v %v; %v %v]", a, b, c, d)
 	if cc == 0 {
+		// The eigenvalues are real, so check that the imaginary parts
+		// are zero.
 		if rt1i != 0 || rt2i != 0 {
 			t.Errorf("Unexpected complex eigenvalues for %v", mat)
 		}
 	} else {
+		// The eigenvalues are complex, so check that documented
+		// conditions hold.
 		if aa != dd {
 			t.Errorf("Diagonal elements not equal for %v: got [%v %v]", mat, aa, dd)
 		}
 		if bb*cc >= 0 {
 			t.Errorf("Non-diagonal elements have the same sign for %v: got [%v %v]", mat, bb, cc)
 		} else {
+			// Compute the absolute value of the imaginary part.
 			im := math.Sqrt(-bb * cc)
+			// Check that ±im is close to one of the returned
+			// imaginary parts.
 			if math.Abs(rt1i-im) > 1e-14 && math.Abs(rt1i+im) > 1e-14 {
 				t.Errorf("Unexpected imaginary part of eigenvalue for %v: got %v, want %v or %v", mat, rt1i, im, -im)
 			}
@@ -80,16 +87,19 @@ func dlanv2Test(t *testing.T, impl Dlanv2er, a, b, c, d float64) {
 			}
 		}
 	}
+	// Check that the returned real parts are consistent.
 	if rt1r != aa && rt1r != dd {
 		t.Errorf("Unexpected real part of eigenvalue for %v: got %v, want %v or %v", mat, rt1r, aa, dd)
 	}
 	if rt2r != aa && rt2r != dd {
 		t.Errorf("Unexpected real part of eigenvalue for %v: got %v, want %v or %v", mat, rt2r, aa, dd)
 	}
+	// Check that the columns of the orthogonal matrix have unit norm.
 	if math.Abs(math.Hypot(cs, sn)-1) > 1e-14 {
 		t.Errorf("Unexpected unitary matrix for %v: got cs %v, sn %v", mat, cs, sn)
 	}
 
+	// Re-compute the original matrix [a b; c d] from its factorization.
 	gota := cs*(aa*cs-bb*sn) - sn*(cc*cs-dd*sn)
 	gotb := cs*(aa*sn+bb*cs) - sn*(cc*sn+dd*cs)
 	gotc := sn*(aa*cs-bb*sn) + cs*(cc*cs-dd*sn)