diff --git a/src/java/org/apache/commons/math/MessagesResources_fr.java b/src/java/org/apache/commons/math/MessagesResources_fr.java
index f6f176895..48e03209d 100644
--- a/src/java/org/apache/commons/math/MessagesResources_fr.java
+++ b/src/java/org/apache/commons/math/MessagesResources_fr.java
@@ -174,8 +174,6 @@ public class MessagesResources_fr
     // org.apache.commons.math.linear.EigenDecompositionImpl
     { "cannot solve degree {0} equation",
       "impossible de r\u00e9soudre une \u00e9quation de degr\u00e9 {0}" },
-    { "negative element on decomposed tridiagonal of {0}x{1} matrix",
-      "\u00e9l\u00e9ment n\u00e9gatif dans la d\u00e9composition tri-diagonale d''une matrice {0}x{1}" },
 
     // org.apache.commons.math.linear.NonSquareMatrixException
     { "a {0}x{1} matrix was provided instead of a square matrix",
@@ -209,6 +207,12 @@ public class MessagesResources_fr
       "tableau des indices de lignes s\u00e9lectionn\u00e9es vide" },
     { "empty selected column index array",
       "tableau des indices de colonnes s\u00e9lectionn\u00e9es vide" },
+    { "{0}x{1} and {2}x{3} matrices are not multiplication compatible",
+      "les dimensions {0}x{1} et {2}x{3} sont incompatibles pour la multiplication matricielle" },
+    { "{0}x{1} and {2}x{3} matrices are not addition compatible",
+      "les dimensions {0}x{1} et {2}x{3} sont incompatibles pour l'addition matricielle" },
+    { "{0}x{1} and {2}x{3} matrices are not subtraction compatible",
+      "les dimensions {0}x{1} et {2}x{3} sont incompatibles pour la soustraction matricielle" },
 
    // org.apache.commons.math.random.EmpiricalDistributionImpl
    // org.apache.commons.math.random.ValueServer
diff --git a/src/java/org/apache/commons/math/linear/RealMatrixImpl.java b/src/java/org/apache/commons/math/linear/RealMatrixImpl.java
index d149f415a..53c3b3a30 100644
--- a/src/java/org/apache/commons/math/linear/RealMatrixImpl.java
+++ b/src/java/org/apache/commons/math/linear/RealMatrixImpl.java
@@ -174,7 +174,12 @@ public class RealMatrixImpl implements RealMatrix, Serializable {
             final int rowCount    = getRowDimension();
             final int columnCount = getColumnDimension();
             if (columnCount != m.getColumnDimension() || rowCount != m.getRowDimension()) {
-                throw new IllegalArgumentException("matrix dimension mismatch");
+                throw MathRuntimeException.createIllegalArgumentException("{0}x{1} and {2}x{3} matrices are not" +
+                                                                          " addition compatible",
+                                                                          new Object[] {
+                                                                              getRowDimension(), getColumnDimension(),
+                                                                              m.getRowDimension(), m.getColumnDimension()
+                                                                          });
             }
             final double[][] outData = new double[rowCount][columnCount];
             for (int row = 0; row < rowCount; row++) {
@@ -199,7 +204,12 @@ public class RealMatrixImpl implements RealMatrix, Serializable {
         final int rowCount    = getRowDimension();
         final int columnCount = getColumnDimension();
         if (columnCount != m.getColumnDimension() || rowCount != m.getRowDimension()) {
-            throw new IllegalArgumentException("matrix dimension mismatch");
+            throw MathRuntimeException.createIllegalArgumentException("{0}x{1} and {2}x{3} matrices are not" +
+                                                                      " addition compatible",
+                                                                      new Object[] {
+                                                                          getRowDimension(), getColumnDimension(),
+                                                                          m.getRowDimension(), m.getColumnDimension()
+                                                                      });
         }
         final double[][] outData = new double[rowCount][columnCount];
         for (int row = 0; row < rowCount; row++) {
@@ -221,7 +231,12 @@ public class RealMatrixImpl implements RealMatrix, Serializable {
             final int rowCount    = getRowDimension();
             final int columnCount = getColumnDimension();
             if (columnCount != m.getColumnDimension() || rowCount != m.getRowDimension()) {
-                throw new IllegalArgumentException("matrix dimension mismatch");
+                throw MathRuntimeException.createIllegalArgumentException("{0}x{1} and {2}x{3} matrices are not" +
+                                                                          " subtraction compatible",
+                                                                          new Object[] {
+                                                                              getRowDimension(), getColumnDimension(),
+                                                                              m.getRowDimension(), m.getColumnDimension()
+                                                                          });
             }
             final double[][] outData = new double[rowCount][columnCount];
             for (int row = 0; row < rowCount; row++) {
@@ -246,7 +261,12 @@ public class RealMatrixImpl implements RealMatrix, Serializable {
         final int rowCount    = getRowDimension();
         final int columnCount = getColumnDimension();
         if (columnCount != m.getColumnDimension() || rowCount != m.getRowDimension()) {
-            throw new IllegalArgumentException("matrix dimension mismatch");
+            throw MathRuntimeException.createIllegalArgumentException("{0}x{1} and {2}x{3} matrices are not" +
+                                                                      " subtraction compatible",
+                                                                      new Object[] {
+                                                                          getRowDimension(), getColumnDimension(),
+                                                                          m.getRowDimension(), m.getColumnDimension()
+                                                                      });
         }
         final double[][] outData = new double[rowCount][columnCount];
         for (int row = 0; row < rowCount; row++) {
@@ -296,7 +316,12 @@ public class RealMatrixImpl implements RealMatrix, Serializable {
             return multiply((RealMatrixImpl) m);
         } catch (ClassCastException cce) {
             if (this.getColumnDimension() != m.getRowDimension()) {
-                throw new IllegalArgumentException("Matrices are not multiplication compatible.");
+                throw MathRuntimeException.createIllegalArgumentException("{0}x{1} and {2}x{3} matrices are not" +
+                                                                          " multiplication compatible",
+                                                                          new Object[] {
+                                                                              getRowDimension(), getColumnDimension(),
+                                                                              m.getRowDimension(), m.getColumnDimension()
+                                                                          });
             }
             final int nRows = this.getRowDimension();
             final int nCols = m.getColumnDimension();
@@ -326,7 +351,12 @@ public class RealMatrixImpl implements RealMatrix, Serializable {
      */
     public RealMatrixImpl multiply(RealMatrixImpl m) throws IllegalArgumentException {
         if (this.getColumnDimension() != m.getRowDimension()) {
-            throw new IllegalArgumentException("Matrices are not multiplication compatible.");
+            throw MathRuntimeException.createIllegalArgumentException("{0}x{1} and {2}x{3} matrices are not" +
+                                                                      " multiplication compatible",
+                                                                      new Object[] {
+                                                                          getRowDimension(), getColumnDimension(),
+                                                                          m.getRowDimension(), m.getColumnDimension()
+                                                                      });
         }
         final int nRows = this.getRowDimension();
         final int nCols = m.getColumnDimension();