Features:

- Square Matrix is Triangularizable (1, 2) - Numerical R^1 -> R^1 Eigenvalue Characteristic Polynomial (3, 4, 5) - Square Matrix Eigenvalue Characteristic Polynomial (6, 7, 8) - Triangular Matrix Remove R2 Array (9, 10) - Triangular Matrix Zero Diagonal Entries (13, 14) - Triangular Matrix Is Uni Check (15, 16) - Triangular Matrix Is Triangularizable Check (19, 20) - Triangular Matrix Determinant and Permanent (21, 22) - Square Matrix Triangular Entries #1 (23, 24) - Square Matrix Triangular Entries #2 (25, 26) - Triangular Matrix Eigenvalue Multiplicity Map (27, 28, 29) - Triangular Matrix Eigenvalue Characteristic Polynomial (30, 31, 32) - Triangular Matrix Is Unit Check (33, 34) - Triangular Matrix Is Normed Check (35, 36) - Triangular Matrix Is Upper Unitriangular (37, 38) - Triangular Matrix Is Lower Unitriangular (39, 40) - Triangular Matrix Atomic Lower #1 (41, 42) - Triangular Matrix Atomic Lower #2 (43, 44) - Triangular Matrix Atomic Lower #3 (45, 46) - Triangular Matrix Atomic Upper #1 (47, 48) - Triangular Matrix Atomic Upper #2 (49, 50) - Triangular Matrix Is Atomic Unitriangular (51, 52) - Triangular Matrix Is Frobenius Unitriangular (53, 54) - Triangular Matrix Is Gauss Unitriangular (55, 56) - Triangular Matrix Gauss Transformation Unitriangular (57, 58) - Linear Algebra Triangular Matrix Constructor (59, 60) - Linear Algebra Triangular Matrix Standard (61, 62, 63) - Linear Algebra Triangular Matrix Type (64) - CRNG Random Matrix Generator Shell (65, 66) - Random Matrix Generator Upper Triangular (67, 68, 69) - Random Matrix Generator Lower Triangular (70, 71, 72) Bug Fixes/Re-organization: - Linear Algebra Triangular Matrix Revamp (11, 12) - Triangular Matrix Determinant/Permanent Revamp (17, 18) - Triangular Matrix Variants and Solutions (73, 74) Samples: - Lower Triangular Matrix Shell #1 (75, 76) - Lower Triangular Matrix Shell #2 (77, 78) - Lower Triangular Matrix Shell #3 (79, 80, 81) - Lower Triangular Matrix Shell #4 (82, 83, 84) - Lower Triangular Matrix Shell #5 (85, 86, 87) - Lower Triangular Matrix Shell #6 (88, 89, 90) - Lower Triangular Matrix Shell #7 (91, 92, 93) - Lower Triangular Matrix Shell #8 (94, 95, 96) - Lower Triangular Matrix Shell #9 (97, 98, 99) - Lower Triangular Matrix Shell #10 (100, 101, 102) - Lower Triangular Matrix Shell #11 (103, 104, 105) - Lower Triangular Matrix Shell #12 (106, 107, 108) - Lower Triangular Matrix Shell #13 (109, 110, 111) - Lower Triangular Matrix Shell #14 (112, 113, 114) - Lower Triangular Matrix Shell #15 (115, 116, 117) - Lower Triangular Matrix Shell #16 (118, 119, 120) IdeaDRIP:
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diff --git a/ReleaseNotes/02_06_2024.txt b/ReleaseNotes/02_06_2024.txt
@@ -0,0 +1,64 @@
+
+Features:
+
+	- Square Matrix is Triangularizable (1, 2)
+	- Numerical R^1 -> R^1 Eigenvalue Characteristic Polynomial (3, 4, 5)
+	- Square Matrix Eigenvalue Characteristic Polynomial (6, 7, 8)
+	- Triangular Matrix Remove R2 Array (9, 10)
+	- Triangular Matrix Zero Diagonal Entries (13, 14)
+	- Triangular Matrix Is Uni Check (15, 16)
+	- Triangular Matrix Is Triangularizable Check (19, 20)
+	- Triangular Matrix Determinant and Permanent (21, 22)
+	- Square Matrix Triangular Entries #1 (23, 24)
+	- Square Matrix Triangular Entries #2 (25, 26)
+	- Triangular Matrix Eigenvalue Multiplicity Map (27, 28, 29)
+	- Triangular Matrix Eigenvalue Characteristic Polynomial (30, 31, 32)
+	- Triangular Matrix Is Unit Check (33, 34)
+	- Triangular Matrix Is Normed Check (35, 36)
+	- Triangular Matrix Is Upper Unitriangular (37, 38)
+	- Triangular Matrix Is Lower Unitriangular (39, 40)
+	- Triangular Matrix Atomic Lower #1 (41, 42)
+	- Triangular Matrix Atomic Lower #2 (43, 44)
+	- Triangular Matrix Atomic Lower #3 (45, 46)
+	- Triangular Matrix Atomic Upper #1 (47, 48)
+	- Triangular Matrix Atomic Upper #2 (49, 50)
+	- Triangular Matrix Is Atomic Unitriangular (51, 52)
+	- Triangular Matrix Is Frobenius Unitriangular (53, 54)
+	- Triangular Matrix Is Gauss Unitriangular (55, 56)
+	- Triangular Matrix Gauss Transformation Unitriangular (57, 58)
+	- Linear Algebra Triangular Matrix Constructor (59, 60)
+	- Linear Algebra Triangular Matrix Standard (61, 62, 63)
+	- Linear Algebra Triangular Matrix Type (64)
+	- CRNG Random Matrix Generator Shell (65, 66)
+	- Random Matrix Generator Upper Triangular (67, 68, 69)
+	- Random Matrix Generator Lower Triangular (70, 71, 72)
+
+
+Bug Fixes/Re-organization:
+
+	- Linear Algebra Triangular Matrix Revamp (11, 12)
+	- Triangular Matrix Determinant/Permanent Revamp (17, 18)
+	- Triangular Matrix Variants and Solutions (73, 74)
+
+
+Samples:
+
+	- Lower Triangular Matrix Shell #1 (75, 76)
+	- Lower Triangular Matrix Shell #2 (77, 78)
+	- Lower Triangular Matrix Shell #3 (79, 80, 81)
+	- Lower Triangular Matrix Shell #4 (82, 83, 84)
+	- Lower Triangular Matrix Shell #5 (85, 86, 87)
+	- Lower Triangular Matrix Shell #6 (88, 89, 90)
+	- Lower Triangular Matrix Shell #7 (91, 92, 93)
+	- Lower Triangular Matrix Shell #8 (94, 95, 96)
+	- Lower Triangular Matrix Shell #9 (97, 98, 99)
+	- Lower Triangular Matrix Shell #10 (100, 101, 102)
+	- Lower Triangular Matrix Shell #11 (103, 104, 105)
+	- Lower Triangular Matrix Shell #12 (106, 107, 108)
+	- Lower Triangular Matrix Shell #13 (109, 110, 111)
+	- Lower Triangular Matrix Shell #14 (112, 113, 114)
+	- Lower Triangular Matrix Shell #15 (115, 116, 117)
+	- Lower Triangular Matrix Shell #16 (118, 119, 120)
+
+
+IdeaDRIP:
diff --git a/src/main/java/org/drip/measure/crng/RandomMatrixGenerator.java b/src/main/java/org/drip/measure/crng/RandomMatrixGenerator.java
@@ -0,0 +1,170 @@
+
+package org.drip.measure.crng;
+
+import org.drip.numerical.linearalgebra.TriangularMatrix;
+
+/*
+ * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+ */
+
+/*!
+ * Copyright (C) 2025 Lakshmi Krishnamurthy
+ * 
+ *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
+ *  	asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
+ *  	analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
+ *  	equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
+ *  	numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
+ *  	graph builder/navigator, and computational support.
+ *  
+ *  	https://lakshmidrip.github.io/DROP/
+ *  
+ *  DROP is composed of three modules:
+ *  
+ *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
+ *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
+ *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
+ * 
+ * 	DROP Product Core implements libraries for the following:
+ * 	- Fixed Income Analytics
+ * 	- Loan Analytics
+ * 	- Transaction Cost Analytics
+ * 
+ * 	DROP Portfolio Core implements libraries for the following:
+ * 	- Asset Allocation Analytics
+ *  - Asset Liability Management Analytics
+ * 	- Capital Estimation Analytics
+ * 	- Exposure Analytics
+ * 	- Margin Analytics
+ * 	- XVA Analytics
+ * 
+ * 	DROP Computational Core implements libraries for the following:
+ * 	- Algorithm Support
+ * 	- Computation Support
+ * 	- Function Analysis
+ *  - Graph Algorithm
+ *  - Model Validation
+ * 	- Numerical Analysis
+ * 	- Numerical Optimizer
+ * 	- Spline Builder
+ *  - Statistical Learning
+ * 
+ * 	Documentation for DROP is Spread Over:
+ * 
+ * 	- Main                     => https://lakshmidrip.github.io/DROP/
+ * 	- Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
+ * 	- GitHub                   => https://github.com/lakshmiDRIP/DROP
+ * 	- Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
+ * 	- Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
+ * 	- Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
+ * 	- Release Versions         => https://lakshmidrip.github.io/DROP/version.html
+ * 	- Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
+ * 	- Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
+ * 
+ *  Licensed 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.
+ */
+
+/**
+ * <i>RandomMatrixGenerator</i> provides Functionality for generating different Kinds of Random Matrices. The
+ *  References are:
+ * 
+ * <br><br>
+ * 	<ul>
+ * 		<li>
+ * 			Axler, S. J. (1997): <i>Linear Algebra Done Right 2<sup>nd</sup> Edition</i> <b>Springer</b>
+ * 				New York NY
+ * 		</li>
+ * 		<li>
+ * 			Bernstein, D. S. (2009): <i>Matrix Mathematics: Theory, Facts, and Formulas 2<sup>nd</sup>
+ * 				Edition</i> <b>Princeton University Press</b> Princeton NJ
+ * 		</li>
+ * 		<li>
+ * 			Herstein, I. N. (1975): <i>Topics in Algebra 2<sup>nd</sup> Edition</i> <b>Wiley</b> New York NY
+ * 		</li>
+ * 		<li>
+ * 			Prasolov, V. V. (1994): <i>Topics in Algebra</i> <b>American Mathematical Society</b> Providence
+ * 				RI
+ * 		</li>
+ * 		<li>
+ * 			Wikipedia (2024): Triangular Matrix https://en.wikipedia.org/wiki/Triangular_matrix
+ * 		</li>
+ * 	</ul>
+ * 
+ * <br><br>
+ *  <ul>
+ *		<li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
+ *		<li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
+ *		<li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/numerical/README.md">Numerical Quadrature, Differentiation, Eigenization, Linear Algebra, and Utilities</a></li>
+ *		<li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/numerical/linearalgebra/README.md">Linear Algebra Matrix Transform Library</a></li>
+ *  </ul>
+ * <br><br>
+ *
+ * @author Lakshmi Krishnamurthy
+ */
+
+public class RandomMatrixGenerator
+{
+
+	/**
+	 * Construct a Lower Triangular Matrix of Random Elements up to the Maximum Value
+	 * 
+	 * @param elementCount Number of Elements in the Array
+	 * @param maximumElement Maximum Element
+	 * @param isEntryInteger TRUE - Entry is an Integer
+	 * 
+	 * @return Lower Triangular Matrix of Random Elements up to the Maximum Value
+	 */
+
+	public static final TriangularMatrix LowerTriangular (
+		final int elementCount,
+		final double maximumElement,
+		final boolean isEntryInteger)
+	{
+		double[][] r2Array = RdRandomSequence.TwoD (elementCount, maximumElement, isEntryInteger);
+
+    	for (int i = 0; i < r2Array.length; ++i) {
+        	for (int j = i + 1; j < r2Array.length; ++j) {
+    			r2Array[i][j] = 0.;
+        	}
+    	}
+
+		return TriangularMatrix.Standard (r2Array);
+	}
+
+	/**
+	 * Construct an Upper Triangular Matrix of Random Elements up to the Maximum Value
+	 * 
+	 * @param elementCount Number of Elements in the Array
+	 * @param maximumElement Maximum Element
+	 * @param isEntryInteger TRUE - Entry is an Integer
+	 * 
+	 * @return Upper Triangular Matrix of Random Elements up to the Maximum Value
+	 */
+
+	public static final TriangularMatrix UpperTriangular (
+		final int elementCount,
+		final double maximumElement,
+		final boolean isEntryInteger)
+	{
+		double[][] r2Array = RdRandomSequence.TwoD (elementCount, maximumElement, isEntryInteger);
+
+    	for (int i = 0; i < r2Array.length; ++i) {
+        	for (int j = 0; j < i; ++j) {
+    			r2Array[i][j] = 0.;
+        	}
+    	}
+
+		return TriangularMatrix.Standard (r2Array);
+	}
+}
diff --git a/src/main/java/org/drip/numerical/eigen/EigenOutput.java b/src/main/java/org/drip/numerical/eigen/EigenOutput.java
@@ -4,6 +4,8 @@
 import java.util.HashMap;
 import java.util.Map;
 
+import org.drip.function.definition.R1ToR1;
+
 /*
  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  */
@@ -197,4 +199,29 @@ public double determinant()
 
 		return determinant;
 	}
+
+	/**
+	 * Retrieve the Characteristic Polynomial of the Eigenvalues
+	 * 
+	 * @return Characteristic Polynomial of the Eigenvalues
+	 */
+
+	public R1ToR1 characteristicPolynomial()
+	{
+		return new R1ToR1 (null)
+		{
+			@Override public double evaluate (
+				final double x)
+				throws Exception
+			{
+				double value = 1.;
+
+				for (double eigenValue : _eigenValueArray) {
+					value *= (x - eigenValue);
+				}
+
+				return value;
+			}
+		};
+	}
 }
diff --git a/src/main/java/org/drip/numerical/linearalgebra/SquareMatrix.java b/src/main/java/org/drip/numerical/linearalgebra/SquareMatrix.java
@@ -3,6 +3,7 @@
 
 import java.util.Map;
 
+import org.drip.function.definition.R1ToR1;
 import org.drip.numerical.common.NumberUtil;
 import org.drip.numerical.eigen.EigenOutput;
 import org.drip.numerical.eigen.QREigenComponentExtractor;
@@ -129,7 +130,7 @@ public class SquareMatrix
 	 * @return Standard Instance of <i>SquareMatrix</i>
 	 */
 
-	public static final SquareMatrix Standard (
+	public static SquareMatrix Standard (
 		final double[][] r2Array)
 	{
 		if (!MatrixUtil.IsSquare (r2Array)) {
@@ -253,6 +254,17 @@ public boolean isNormal()
 		return true;
 	}
 
+	/**
+	 * Calculate whether the Matrix is "Triangularizable"
+	 * 
+	 * @return TRUE - Matrix is "Triangularizable"
+	 */
+
+	public boolean isTriangularizable()
+	{
+		return true;
+	}
+
 	/**
 	 * Eigenize and Extract the Components of the Specified Matrix
 	 * 
@@ -264,6 +276,23 @@ public EigenOutput eigenize()
 		return QREigenComponentExtractor.Standard().eigenize (_r2Array);
 	}
 
+	/**
+	 * Retrieve the Array of Diagonal Entries
+	 * 
+	 * @return Array of Diagonal Entries
+	 */
+
+	public double[] diagonalEntryArray()
+	{
+		double[] diagonalEntryArray = new double[_r2Array.length];
+
+		for (int i = 0; i < _r2Array.length; ++i) {
+			diagonalEntryArray[i] = _r2Array[i][i];
+		}
+
+		return diagonalEntryArray;
+	}
+
 	/**
 	 * Retrieve the Eigenvalue Multiplicity Map
 	 * 
@@ -296,4 +325,17 @@ public double determinant()
 
 		return eigenOutput.determinant();
 	}
+
+	/**
+	 * Retrieve the Characteristic Polynomial of the Eigenvalues
+	 * 
+	 * @return Characteristic Polynomial of the Eigenvalues
+	 */
+
+	public R1ToR1 characteristicPolynomial()
+	{
+		EigenOutput eigenOutput = QREigenComponentExtractor.Standard().eigenize (_r2Array);
+
+		return null == eigenOutput ? null : eigenOutput.characteristicPolynomial();
+	}
 }