perf(math): route ordinary products through MKL and preserve arithmetic

tests/unit/math/dense_blas_internal_test.cpp

@@ -5,6 +5,7 @@
 #include <array>
 #include <cstddef>
 #include <limits>
+#include <stdexcept>
 
 namespace fesa::dense_blas_internal {
 namespace {
@@ -35,5 +36,26 @@ TEST(DenseBlasInternal, CDup003CopiesZeroAndNonzeroContiguousValues) {
   EXPECT_EQ(destination, source);
 }
 
+TEST(DenseBlasInternal, TransposeProductChecksShapeAndKnownRectangularAction) {
+  Matrix left{3U, 2U};
+  Matrix right{3U, 1U};
+  for (std::size_t row = 0; row < 3U; ++row) {
+    left(row, 0U) = static_cast<double>(row + 1U);
+    left(row, 1U) = 2.0;
+    right(row, 0U) = static_cast<double>(row);
+  }
+  const auto product = MultiplyTransposeLeft(left, right);
+  ASSERT_EQ(product.Rows(), 2U);
+  ASSERT_EQ(product.Columns(), 1U);
+  EXPECT_DOUBLE_EQ(product(0U, 0U), 8.0);
+  EXPECT_DOUBLE_EQ(product(1U, 0U), 6.0);
+  EXPECT_THROW(static_cast<void>(MultiplyTransposeLeft(left, Matrix{2U, 1U})),
+               std::invalid_argument);
+  const auto empty = MultiplyTransposeLeft(Matrix{0U, 2U}, Matrix{0U, 3U});
+  EXPECT_EQ(empty.Rows(), 2U);
+  EXPECT_EQ(empty.Columns(), 3U);
+  EXPECT_DOUBLE_EQ(empty(1U, 2U), 0.0);
+}
+
 }  // namespace
 }  // namespace fesa::dense_blas_internal