diff --git a/wpimath/src/main/java/edu/wpi/first/math/estimator/ExtendedKalmanFilter.java b/wpimath/src/main/java/edu/wpi/first/math/estimator/ExtendedKalmanFilter.java
index 055bf9939a..fa8f9245e9 100644
--- a/wpimath/src/main/java/edu/wpi/first/math/estimator/ExtendedKalmanFilter.java
+++ b/wpimath/src/main/java/edu/wpi/first/math/estimator/ExtendedKalmanFilter.java
@@ -372,7 +372,11 @@ public class ExtendedKalmanFilter<States extends Num, Inputs extends Num, Output
     //
     // Kᵀ = Sᵀ.solve(CPᵀ)
     // K = (Sᵀ.solve(CPᵀ))ᵀ
-    final Matrix<States, Rows> K = S.transpose().solve(C.times(m_P.transpose())).transpose();
+    //
+    // Drop the transposes on symmetric matrices S and P.
+    //
+    // K = (S.solve(CP))ᵀ
+    final Matrix<States, Rows> K = S.solve(C.times(m_P)).transpose();
 
     // x̂ₖ₊₁⁺ = x̂ₖ₊₁⁻ + K(y − h(x̂ₖ₊₁⁻, uₖ₊₁))
     m_xHat = addFuncX.apply(m_xHat, K.times(residualFuncY.apply(y, h.apply(m_xHat, u))));
diff --git a/wpimath/src/main/java/edu/wpi/first/math/estimator/KalmanFilter.java b/wpimath/src/main/java/edu/wpi/first/math/estimator/KalmanFilter.java
index 40e6c96c7a..2d76cabfee 100644
--- a/wpimath/src/main/java/edu/wpi/first/math/estimator/KalmanFilter.java
+++ b/wpimath/src/main/java/edu/wpi/first/math/estimator/KalmanFilter.java
@@ -230,7 +230,11 @@ public class KalmanFilter<States extends Num, Inputs extends Num, Outputs extend
     //
     // Kᵀ = Sᵀ.solve(CPᵀ)
     // K = (Sᵀ.solve(CPᵀ))ᵀ
-    final Matrix<States, Outputs> K = S.transpose().solve(C.times(m_P.transpose())).transpose();
+    //
+    // Drop the transposes on symmetric matrices S and P.
+    //
+    // K = (S.solve(CP))ᵀ
+    final Matrix<States, Outputs> K = S.solve(C.times(m_P)).transpose();
 
     // x̂ₖ₊₁⁺ = x̂ₖ₊₁⁻ + K(y − (Cx̂ₖ₊₁⁻ + Duₖ₊₁))
     m_xHat = m_xHat.plus(K.times(y.minus(C.times(m_xHat).plus(D.times(u)))));
diff --git a/wpimath/src/main/java/edu/wpi/first/math/estimator/SteadyStateKalmanFilter.java b/wpimath/src/main/java/edu/wpi/first/math/estimator/SteadyStateKalmanFilter.java
index 31649728e2..4b5ca7bc65 100644
--- a/wpimath/src/main/java/edu/wpi/first/math/estimator/SteadyStateKalmanFilter.java
+++ b/wpimath/src/main/java/edu/wpi/first/math/estimator/SteadyStateKalmanFilter.java
@@ -100,9 +100,11 @@ public class SteadyStateKalmanFilter<States extends Num, Inputs extends Num, Out
     //
     // Kᵀ = Sᵀ.solve(CPᵀ)
     // K = (Sᵀ.solve(CPᵀ))ᵀ
-    m_K =
-        new Matrix<>(
-            S.transpose().getStorage().solve(C.times(P.transpose()).getStorage()).transpose());
+    //
+    // Drop the transposes on symmetric matrices S and P.
+    //
+    // K = (S.solve(CP))ᵀ
+    m_K = new Matrix<>(S.getStorage().solve(C.times(P).getStorage()).transpose());
 
     reset();
   }
diff --git a/wpimath/src/main/native/include/frc/DARE.h b/wpimath/src/main/native/include/frc/DARE.h
index fba06ccb0a..feca99a1fd 100644
--- a/wpimath/src/main/native/include/frc/DARE.h
+++ b/wpimath/src/main/native/include/frc/DARE.h
@@ -128,7 +128,11 @@ Eigen::Matrix<double, States, States> DARE(
     //
     // V₂ᵀ = W.solve(Gₖᵀ)
     // V₂ = W.solve(Gₖᵀ)ᵀ
-    StateMatrix V_2 = W_solver.solve(G_k.transpose()).transpose();
+    //
+    // Since W, Gₖ, and Hₖ are symmetric, drop the transposes on Gₖ and V₂.
+    //
+    // V₂ = W.solve(Gₖ)
+    StateMatrix V_2 = W_solver.solve(G_k);
 
     // Gₖ₊₁ = Gₖ + AₖV₂Aₖᵀ
     // Hₖ₊₁ = Hₖ + V₁ᵀHₖAₖ
diff --git a/wpimath/src/main/native/include/frc/estimator/ExtendedKalmanFilter.h b/wpimath/src/main/native/include/frc/estimator/ExtendedKalmanFilter.h
index ccf8f935c4..22eddbc281 100644
--- a/wpimath/src/main/native/include/frc/estimator/ExtendedKalmanFilter.h
+++ b/wpimath/src/main/native/include/frc/estimator/ExtendedKalmanFilter.h
@@ -397,8 +397,11 @@ class ExtendedKalmanFilter {
     //
     // Kᵀ = Sᵀ.solve(CPᵀ)
     // K = (Sᵀ.solve(CPᵀ))ᵀ
-    Matrixd<States, Rows> K =
-        S.transpose().ldlt().solve(C * m_P.transpose()).transpose();
+    //
+    // Drop the transposes on symmetric matrices S and P.
+    //
+    // K = (S.solve(CP))ᵀ
+    Matrixd<States, Rows> K = S.ldlt().solve(C * m_P).transpose();
 
     // x̂ₖ₊₁⁺ = x̂ₖ₊₁⁻ + Kₖ₊₁(y − h(x̂ₖ₊₁⁻, uₖ₊₁))
     m_xHat = addFuncX(m_xHat, K * residualFuncY(y, h(m_xHat, u)));
diff --git a/wpimath/src/main/native/include/frc/estimator/KalmanFilter.h b/wpimath/src/main/native/include/frc/estimator/KalmanFilter.h
index 5f52c810ac..aa169368bb 100644
--- a/wpimath/src/main/native/include/frc/estimator/KalmanFilter.h
+++ b/wpimath/src/main/native/include/frc/estimator/KalmanFilter.h
@@ -235,8 +235,11 @@ class KalmanFilter {
     //
     // Kᵀ = Sᵀ.solve(CPᵀ)
     // K = (Sᵀ.solve(CPᵀ))ᵀ
-    Matrixd<States, Outputs> K =
-        S.transpose().ldlt().solve(C * m_P.transpose()).transpose();
+    //
+    // Drop the transposes on symmetric matrices S and P.
+    //
+    // K = (S.solve(CP))ᵀ
+    Matrixd<States, Outputs> K = S.ldlt().solve(C * m_P).transpose();
 
     // x̂ₖ₊₁⁺ = x̂ₖ₊₁⁻ + K(y − (Cx̂ₖ₊₁⁻ + Duₖ₊₁))
     m_xHat += K * (y - (C * m_xHat + D * u));
diff --git a/wpimath/src/main/native/include/frc/estimator/SteadyStateKalmanFilter.h b/wpimath/src/main/native/include/frc/estimator/SteadyStateKalmanFilter.h
index a705de92bf..734c70c7e0 100644
--- a/wpimath/src/main/native/include/frc/estimator/SteadyStateKalmanFilter.h
+++ b/wpimath/src/main/native/include/frc/estimator/SteadyStateKalmanFilter.h
@@ -114,7 +114,11 @@ class SteadyStateKalmanFilter {
       //
       // Kᵀ = Sᵀ.solve(CPᵀ)
       // K = (Sᵀ.solve(CPᵀ))ᵀ
-      m_K = S.transpose().ldlt().solve(C * P.value().transpose()).transpose();
+      //
+      // Drop the transposes on symmetric matrices S and P.
+      //
+      // K = (S.solve(CP))ᵀ
+      m_K = S.ldlt().solve(C * P.value()).transpose();
     } else if (P.error() == DAREError::QNotSymmetric ||
                P.error() == DAREError::QNotPositiveSemidefinite) {
       std::string msg =