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diff --git a/src/main/java/org/apache/commons/math3/linear/DecompositionSolver.java b/src/main/java/org/apache/commons/math3/linear/DecompositionSolver.java
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+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.math3.linear;
+
+/**
+ * Interface handling decomposition algorithms that can solve A &times; X = B.
+ *
+ * <p>Decomposition algorithms decompose an A matrix has a product of several specific matrices from
+ * which they can solve A &times; X = B in least squares sense: they find X such that ||A &times; X
+ * - B|| is minimal.
+ *
+ * <p>Some solvers like {@link LUDecomposition} can only find the solution for square matrices and
+ * when the solution is an exact linear solution, i.e. when ||A &times; X - B|| is exactly 0. Other
+ * solvers can also find solutions with non-square matrix A and with non-null minimal norm. If an
+ * exact linear solution exists it is also the minimal norm solution.
+ *
+ * @since 2.0
+ */
+public interface DecompositionSolver {
+
+    /**
+     * Solve the linear equation A &times; X = B for matrices A.
+     *
+     * <p>The A matrix is implicit, it is provided by the underlying decomposition algorithm.
+     *
+     * @param b right-hand side of the equation A &times; X = B
+     * @return a vector X that minimizes the two norm of A &times; X - B
+     * @throws org.apache.commons.math3.exception.DimensionMismatchException if the matrices
+     *     dimensions do not match.
+     * @throws SingularMatrixException if the decomposed matrix is singular.
+     */
+    RealVector solve(final RealVector b) throws SingularMatrixException;
+
+    /**
+     * Solve the linear equation A &times; X = B for matrices A.
+     *
+     * <p>The A matrix is implicit, it is provided by the underlying decomposition algorithm.
+     *
+     * @param b right-hand side of the equation A &times; X = B
+     * @return a matrix X that minimizes the two norm of A &times; X - B
+     * @throws org.apache.commons.math3.exception.DimensionMismatchException if the matrices
+     *     dimensions do not match.
+     * @throws SingularMatrixException if the decomposed matrix is singular.
+     */
+    RealMatrix solve(final RealMatrix b) throws SingularMatrixException;
+
+    /**
+     * Check if the decomposed matrix is non-singular.
+     *
+     * @return true if the decomposed matrix is non-singular.
+     */
+    boolean isNonSingular();
+
+    /**
+     * Get the <a
+     * href="http://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_pseudoinverse">pseudo-inverse</a> of
+     * the decomposed matrix.
+     *
+     * <p><em>This is equal to the inverse of the decomposed matrix, if such an inverse exists.</em>
+     *
+     * <p>If no such inverse exists, then the result has properties that resemble that of an
+     * inverse.
+     *
+     * <p>In particular, in this case, if the decomposed matrix is A, then the system of equations
+     * \( A x = b \) may have no solutions, or many. If it has no solutions, then the pseudo-inverse
+     * \( A^+ \) gives the "closest" solution \( z = A^+ b \), meaning \( \left \| A z - b \right
+     * \|_2 \) is minimized. If there are many solutions, then \( z = A^+ b \) is the smallest
+     * solution, meaning \( \left \| z \right \|_2 \) is minimized.
+     *
+     * <p>Note however that some decompositions cannot compute a pseudo-inverse for all matrices.
+     * For example, the {@link LUDecomposition} is not defined for non-square matrices to begin
+     * with. The {@link QRDecomposition} can operate on non-square matrices, but will throw {@link
+     * SingularMatrixException} if the decomposed matrix is singular. Refer to the javadoc of
+     * specific decomposition implementations for more details.
+     *
+     * @return pseudo-inverse matrix (which is the inverse, if it exists), if the decomposition can
+     *     pseudo-invert the decomposed matrix
+     * @throws SingularMatrixException if the decomposed matrix is singular and the decomposition
+     *     can not compute a pseudo-inverse
+     */
+    RealMatrix getInverse() throws SingularMatrixException;
+}