diff --git a/test/general/test_matrices.cpp b/test/general/test_matrices.cpp
new file mode 100644
index 0000000000..292ff74230
--- /dev/null
+++ b/test/general/test_matrices.cpp
@@ -0,0 +1,105 @@
+#include "gtest/gtest.h"
+#include "cantera/numerics/BandMatrix.h"
+
+using namespace Cantera;
+
+class BandMatrixTest : public testing::Test
+{
+public:
+    BandMatrixTest()
+        : x{1,2,3,4,5,6}
+        , b1{-8, -8, 6, 40, 149, 81}
+        , b2{1, 8, 30, 72, 140, 65}
+        , v1{3, 13, 28, 55, 100, 92}
+        , v2{0, 5, 16, 39, 115, 116}
+    {
+        A1.resize(6, 1, 2); // one lower, two upper
+        A2.resize(6, 2, 1); // two lower, one upper
+        // main diagonal
+        for (size_t i = 0; i < 6; i++) {
+            A1(i, i) = i + 1;
+            A2(i, i) = i + 1;
+        }
+
+        // first subdiagonal and superdiagonal
+        for (size_t i = 0; i < 5; i++) {
+            A1(i+1, i) = 2 * i + 1;
+            A1(i, i+1) = i * i;
+            A2(i+1, i) = 2 * i + 1;
+            A2(i, i+1) = i * i;
+        }
+
+        // second subdiagonal and superdiagonal
+        for (size_t i = 0; i < 4; i++) {
+            A1(i, i+2) = - static_cast<int>(i + 3);
+            A2(i+2, i) = - static_cast<int>(i + 1);
+        }
+    }
+
+    BandMatrix A1, A2;
+    vector_fp x;
+    vector_fp b1, b2;
+    vector_fp v1, v2;
+};
+
+TEST_F(BandMatrixTest, matrix_times_vector)
+{
+    vector_fp c(6, 0.0);
+    A1.mult(x.data(), c.data());
+    for (size_t i = 0; i < 6; i++) {
+        EXPECT_DOUBLE_EQ(b1[i], c[i]);
+    }
+    A2.mult(x.data(), c.data());
+    for (size_t i = 0; i < 6; i++) {
+        EXPECT_DOUBLE_EQ(b2[i], c[i]);
+    }
+}
+
+TEST_F(BandMatrixTest, vector_times_matrix)
+{
+    vector_fp c(6, 0.0);
+    A1.leftMult(x.data(), c.data());
+    for (size_t i = 0; i < 6; i++) {
+        EXPECT_DOUBLE_EQ(v1[i], c[i]);
+    }
+    A2.leftMult(x.data(), c.data());
+    for (size_t i = 0; i < 6; i++) {
+        EXPECT_DOUBLE_EQ(v2[i], c[i]);
+    }
+}
+
+TEST_F(BandMatrixTest, solve_linear_system)
+{
+    vector_fp c(6, 0.0);
+    A1.solve(b1.data(), c.data());
+    for (size_t i = 0; i < 6; i++) {
+        EXPECT_NEAR(x[i], c[i], 1e-10);
+    }
+    A2.solve(b2.data(), c.data());
+    for (size_t i = 0; i < 6; i++) {
+        EXPECT_NEAR(x[i], c[i], 1e-10);
+    }
+}
+
+TEST_F(BandMatrixTest, oneNorm) {
+
+    EXPECT_DOUBLE_EQ(28, A1.oneNorm());
+    EXPECT_DOUBLE_EQ(23, A2.oneNorm());
+}
+
+TEST_F(BandMatrixTest, checkRowsColumns) {
+    double s;
+    size_t i = A1.checkRows(s);
+    EXPECT_EQ((size_t) 0, i);
+    EXPECT_DOUBLE_EQ(3, s);
+    i = A2.checkRows(s);
+    EXPECT_EQ((size_t) 0, i);
+    EXPECT_DOUBLE_EQ(1, s);
+
+    i = A1.checkColumns(s);
+    EXPECT_EQ((size_t) 0, i);
+    EXPECT_DOUBLE_EQ(1, s);
+    i = A2.checkColumns(s);
+    EXPECT_EQ((size_t) 0, i);
+    EXPECT_DOUBLE_EQ(1, s);
+}