diff --git a/RELEASE_NOTES.md b/RELEASE_NOTES.md
index cf5f86a..7443e53 100644
--- a/RELEASE_NOTES.md
+++ b/RELEASE_NOTES.md
@@ -2,6 +2,10 @@
 
 ## [Unreleased]
 
+### Added
+
+- Add left_multiplication and right_multiplication to ThreadingInstructions (#99)
+
 ### Changed
 
 - Build wheels on macOS 14 for arm64 and macOS 15 for x86_64 (#108)
diff --git a/src/ThreadingInstructions.cpp b/src/ThreadingInstructions.cpp
index 121fde0..4ba5be4 100644
--- a/src/ThreadingInstructions.cpp
+++ b/src/ThreadingInstructions.cpp
@@ -15,7 +15,9 @@
 // along with this program.  If not, see <http://www.gnu.org/licenses/>.
 
 #include "ThreadingInstructions.hpp"
+#include "GenotypeIterator.hpp"
 
+#include <cmath>
 #include <iostream>
 #include <limits>
 #include <vector>
@@ -259,3 +261,169 @@ ThreadingInstructions ThreadingInstructions::sub_range(const int range_start, co
         std::move(range_positions)
     };
 }
+
+std::vector<double> ThreadingInstructions::left_multiply(const std::vector<double>& x, bool diploid, bool normalize) {
+    // Left-multiplication of the genotype matrix by a vector of doubles
+
+    // Check input vector lengths are correct
+    if (diploid) {
+        if (x.size() != num_samples / 2) {
+            std::ostringstream oss;
+            oss << "Input vector must have length " << num_samples / 2 << ".";
+            throw std::runtime_error(oss.str());
+        }
+    } else {
+        if (x.size() != num_samples) {
+            std::ostringstream oss;
+            oss << "Input vector must have length " << num_samples << ".";
+            throw std::runtime_error(oss.str());
+        }
+    }
+
+    // Initialize genotype traversal
+    GenotypeIterator gi = GenotypeIterator(*this);
+    std::size_t site_counter = 0;
+    std::vector<double> out(num_sites);
+
+    while (gi.has_next_genotype()) {
+        // Fetch the next genotype
+        const std::vector<int>& g = gi.next_genotype();
+
+        // Initialize the next entry
+        double entry = 0.0;
+
+        if (normalize) {
+            // If we want to normalize, we need the mean and standard deviation of g.
+            double ac = 0.0;
+            for (auto a : g) {
+                ac += a;
+            }
+            if (diploid) {
+                // We do the diploid standard deviation by hand
+                double mu = 2.0 * ac / num_samples;
+                double sample_var = 0.0;
+                for (std::size_t i=0; i < x.size(); i++) {
+                    int h = g[2 * i] + g[2 * i + 1];
+                    double d = h - mu;
+                    sample_var += d * d;
+                }
+                sample_var /= (num_samples / 2);
+
+                double std = std::sqrt(sample_var);
+                for (std::size_t i=0; i < x.size(); i++) {
+                    int h = g[2 * i] + g[2 * i + 1];
+                    double w = x[i];
+                    entry += w * (h - mu) / std;
+                }
+            } else {
+                double mu = ac / num_samples;
+                double std = std::sqrt(mu * (1 - mu));
+                for (std::size_t i=0; i < g.size(); i++) {
+                    double w = x[i];
+                    entry += w * (g[i] - mu) / std;
+                }
+            }
+        } else {
+            for (std::size_t i=0; i < g.size(); i++) {
+                double w = diploid ? x[i / 2] : x[i];
+                entry += w * g[i];
+            }
+        }
+        out[site_counter] = entry;
+        site_counter++;
+    }
+    return out;
+}
+
+std::vector<double> ThreadingInstructions::right_multiply(const std::vector<double>& x, bool diploid, bool normalize) {
+    // Right-multiplication of the genotype matrix by a vector of doubles
+
+    // Check input vector lengths are correct
+    if (x.size() != num_sites) {
+        std::ostringstream oss;
+        oss << "Input vector must have length " << num_samples / 2 << ".";
+        throw std::runtime_error(oss.str());
+    }
+
+    GenotypeIterator gi = GenotypeIterator(*this);
+    std::size_t site_counter = 0;
+    if (diploid) {
+        // Initialize output
+        std::vector<double> out(num_samples / 2, 0.0);
+        if (normalize) {
+            while (gi.has_next_genotype()) {
+                // Fetch the next genotype
+                const std::vector<int>& g = gi.next_genotype();
+
+                // If we want to normalize, we need the mean and standard deviation of g.
+                double ac = 0.0;
+                for (auto a : g) {
+                    ac += a;
+                }
+
+                // We do the diploid standard deviation by hand
+                const double mu = 2.0 * ac / num_samples;
+                double sample_var = 0.0;
+                for (std::size_t i=0; i < out.size(); i++) {
+                    int h = g[2 * i] + g[2 * i + 1];
+                    double d = h - mu;
+                    sample_var += d * d;
+                }
+                sample_var /= (num_samples / 2);
+                const double std = std::sqrt(sample_var);
+
+                const double w = x[site_counter] / std;
+                for (std::size_t i=0; i < out.size(); i++) {
+                    const int h = g[2 * i] + g[2 * i + 1];
+                    out[i] += w * (h - mu);
+                }
+                site_counter++;
+            }
+        } else {
+            while (gi.has_next_genotype()) {
+                // Fetch the next genotype
+                const std::vector<int>& g = gi.next_genotype();
+                const double w = x[site_counter];
+                for (std::size_t i=0; i < out.size(); i++) {
+                    const int h = g[2 * i] + g[2 * i + 1];
+                    out[i] += w * h;
+                }
+                site_counter++;
+            }
+        }
+        return out;
+    } else {
+        // Initialize output
+        std::vector<double> out(num_samples, 0.0);
+        if (normalize) {
+            while (gi.has_next_genotype()) {
+                // Fetch the next genotype
+                const std::vector<int>& g = gi.next_genotype();
+                double ac = 0.0;
+                for (auto a : g) {
+                    ac += a;
+                }
+
+                // Normalization constants
+                double mu = ac / num_samples;
+                double std = std::sqrt(mu * (1 - mu));
+                const double w = x[site_counter] / std;
+                for (std::size_t i=0; i < out.size(); i++) {
+                    out[i] += w * (g[i] - mu);
+                }
+                site_counter++;
+            }
+        } else {
+            while (gi.has_next_genotype()) {
+                // Fetch the next genotype
+                const std::vector<int>& g = gi.next_genotype();
+                const double w = x[site_counter];
+                for (std::size_t i=0; i < out.size(); i++) {
+                    out[i] += w * g[i];
+                }
+                site_counter++;
+            }
+        }
+        return out;
+    }
+}
diff --git a/src/ThreadingInstructions.hpp b/src/ThreadingInstructions.hpp
index ae0136b..f404be2 100644
--- a/src/ThreadingInstructions.hpp
+++ b/src/ThreadingInstructions.hpp
@@ -85,6 +85,10 @@ class ThreadingInstructions {
 
     ThreadingInstructions sub_range(const int range_start, const int range_end) const;
 
+    // Common operations
+    std::vector<double> left_multiply(const std::vector<double>& x, bool diploid=false, bool normalize=false);
+    std::vector<double> right_multiply(const std::vector<double>& x, bool diploid=false, bool normalize=false);
+
 public:
     int start = 0;
     int end = 0;
diff --git a/src/threads_arg_pybind.cpp b/src/threads_arg_pybind.cpp
index b8ca12d..c829a20 100644
--- a/src/threads_arg_pybind.cpp
+++ b/src/threads_arg_pybind.cpp
@@ -140,7 +140,9 @@ PYBIND11_MODULE(threads_arg_python_bindings, m) {
       .def("sub_range", &ThreadingInstructions::sub_range)
       .def(py::pickle(
            &threading_instructions_get_state,
-           &threading_instructions_set_state));
+           &threading_instructions_set_state))
+      .def("left_multiply", &ThreadingInstructions::left_multiply, py::arg("x"), py::arg("diploid") = false, py::arg("normalize") = false)
+      .def("right_multiply", &ThreadingInstructions::right_multiply, py::arg("x"), py::arg("diploid") = false, py::arg("normalize") = false);
 
   py::class_<ConsistencyWrapper>(m, "ConsistencyWrapper")
       .def(py::init<const std::vector<std::vector<int>>&, const std::vector<std::vector<double>>&, const std::vector<std::vector<int>>&,
diff --git a/test/test_multiply.py b/test/test_multiply.py
new file mode 100644
index 0000000..9b2e1e5
--- /dev/null
+++ b/test/test_multiply.py
@@ -0,0 +1,117 @@
+# This file is part of the Threads software suite.
+# Copyright (C) 2024-2025 Threads Developers.
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+import numpy as np
+import pgenlib
+import pytest 
+
+from threads_arg.serialization import load_instructions
+
+from snapshot_runners import (
+    TEST_DATA_DIR
+)
+
+def _col_normalize(x):
+    z = x.copy()
+    mu = z.mean(axis=0, keepdims=True)
+    std = z.std(axis=0, keepdims=True)
+    return (z - mu) / std
+
+def test_left_multiply():
+    # Read ground truth genotypes
+    pgen_path = str(TEST_DATA_DIR / "panel.pgen")
+    reader = pgenlib.PgenReader(str(pgen_path).encode())
+    expected_num_variants = reader.get_variant_ct()
+    num_samples = reader.get_raw_sample_ct()
+    expected_gt = np.empty((expected_num_variants, 2 * num_samples), dtype=np.int32)
+    reader.read_alleles_range(0, expected_num_variants, expected_gt)
+    gt_matrix = expected_gt.transpose()
+    gt_matrix_dip = gt_matrix[::2] + gt_matrix[1::2]
+    gt_matrix_norm = _col_normalize(gt_matrix)
+    gt_matrix_dip_norm = _col_normalize(gt_matrix_dip)
+
+    # Read threading instructions
+    threads_path = str(TEST_DATA_DIR / "expected_infer_snapshot.threads")
+    instructions = load_instructions(threads_path)
+
+    # Random vector to multiply with
+    rng = np.random.default_rng(130222)
+    x_hap = rng.normal(0, 1, 2 * num_samples)
+    x_dip = rng.normal(0, 1, num_samples)
+
+    # Make sure length checks are performed
+    with pytest.raises(RuntimeError):
+        instructions.left_multiply(x_dip)
+    with pytest.raises(RuntimeError):
+        instructions.left_multiply(x_hap, diploid=True)
+
+    # Do normal left-multiplication
+    expected = x_hap @ gt_matrix
+    expected_norm = x_hap @ gt_matrix_norm
+    expected_dip = x_dip @ gt_matrix_dip
+    expected_dip_norm = x_dip @ gt_matrix_dip_norm
+
+    # Do threads left-multiplication and confirm results are correct
+    found = instructions.left_multiply(x_hap)
+    assert np.allclose(expected, found)
+    found_norm = instructions.left_multiply(x_hap, normalize=True)
+    assert np.allclose(expected_norm, found_norm)
+    found_dip = instructions.left_multiply(x_dip, diploid=True)
+    assert np.allclose(expected_dip, found_dip)
+    found_dip_norm = instructions.left_multiply(x_dip, normalize=True, diploid=True)
+    assert np.allclose(expected_dip_norm, found_dip_norm)
+
+def test_right_multiply():
+    # Read ground truth genotypes
+    pgen_path = str(TEST_DATA_DIR / "panel.pgen")
+    reader = pgenlib.PgenReader(str(pgen_path).encode())
+    expected_num_variants = reader.get_variant_ct()
+    num_samples = reader.get_raw_sample_ct()
+    expected_gt = np.empty((expected_num_variants, 2 * num_samples), dtype=np.int32)
+    reader.read_alleles_range(0, expected_num_variants, expected_gt)
+    gt_matrix = expected_gt.transpose()
+    gt_matrix_dip = gt_matrix[::2] + gt_matrix[1::2]
+    gt_matrix_norm = _col_normalize(gt_matrix)
+    gt_matrix_dip_norm = _col_normalize(gt_matrix_dip)
+
+    # Read threading instructions
+    threads_path = str(TEST_DATA_DIR / "expected_infer_snapshot.threads")
+    instructions = load_instructions(threads_path)
+
+    # Random vector to multiply with
+    rng = np.random.default_rng(130222)
+    x = rng.normal(0, 1, expected_num_variants)
+    x_wrong_length = rng.normal(0, 1, expected_num_variants + 1)
+
+    # Make sure length check is performed
+    with pytest.raises(RuntimeError):
+        instructions.left_multiply(x_wrong_length)
+
+    # Do normal right-multiplication
+    expected = gt_matrix @ x
+    expected_norm = gt_matrix_norm @ x
+    expected_dip = gt_matrix_dip @ x
+    expected_dip_norm = gt_matrix_dip_norm @ x
+
+    # Do threads right-multiplication and confirm results are correct
+    found = instructions.right_multiply(x)
+    assert np.allclose(expected, found)
+    found_norm = instructions.right_multiply(x, normalize=True)
+    assert np.allclose(expected_norm, found_norm)
+    found_dip = instructions.right_multiply(x, diploid=True)
+    assert np.allclose(expected_dip, found_dip)
+    found_dip_norm = instructions.right_multiply(x, normalize=True, diploid=True)
+    assert np.allclose(expected_dip_norm, found_dip_norm)