Matrix Minors and Cofactors Convenience Methods

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+      "Bash(*)",
+      "WebFetch(*)",
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.gitignore

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-.idea
-vendor/
-composer.lock
-build
-.phpunit.result.cache
-site
-tools/
-.php-cs-fixer.cache
-.phive/
-phive.phar.asc
+.idea
+vendor/
+composer.lock
+build
+.phpunit.result.cache
+site
+tools/
+.php-cs-fixer.cache
+.phive/
+phive.phar.asc
+
+# Auto Claude data directory
+.auto-claude/

src/Samsara/Fermat/LinearAlgebra/Types/Matrix.php

@@ -59,16 +59,21 @@ public function getDeterminant(): ImmutableDecimal
             );
         }
 
-        if ($this->numRows > 2) {
+        if ($this->numRows === 0) {
+            // The determinant of a 0x0 matrix is defined as 1 by convention
+            $determinant = Numbers::makeOne();
+        } elseif ($this->numRows === 1) {
+            $determinant = $this->rows[0]->get(0);
+        } elseif ($this->numRows === 2) {
+            $determinant = $this->rows[0]->get(0)->multiply($this->rows[1]->get(1))->subtract($this->rows[1]->get(0)->multiply($this->rows[0]->get(1)));
+        } else {
             $determinant = Numbers::makeZero();
 
             foreach ($this->rows[0]->toArray() as $key => $value) {
                 $childMatrix = $this->childMatrix(0, $key);
 
                 $determinant = $determinant->add($value->multiply($childMatrix->getDeterminant())->multiply(SequenceProvider::nthPowerNegativeOne($key)));
             }
-        } else {
-            $determinant = $this->rows[0]->get(0)->multiply($this->rows[1]->get(1))->subtract($this->rows[1]->get(0)->multiply($this->rows[0]->get(1)));
         }
 
         return $determinant;
@@ -84,7 +89,6 @@ public function getInverseMatrix(): static
         $determinant = $this->getDeterminant();
         $inverseDeterminant = new ImmutableFraction(Numbers::makeOne(), $determinant);
 
-        // TODO: Implement minors & cofactors method https://www.mathsisfun.com/algebra/matrix-inverse-minors-cofactors-adjugate.html
         if ($this->getRowCount() > 2) {
             $minors = $this->getMatrixOfMinors();
             $cofactors = $minors->applyAlternatingSigns();
@@ -114,6 +118,31 @@ public function getMatrixOfMinors(): static
         return $this->mapFuction($fn);
     }
 
+    /**
+     * Returns a new collection that contains the matrix of minors for each element in the current collection.
+     *
+     * This is an alias for getMatrixOfMinors().
+     *
+     * @return static A new collection containing the matrix of minors.
+     */
+    public function minors(): static
+    {
+        return $this->getMatrixOfMinors();
+    }
+
+    /**
+     * Returns a new matrix containing the cofactors of each element in the current matrix.
+     *
+     * The matrix of cofactors is obtained by taking the matrix of minors and applying alternating signs
+     * based on position. The sign pattern follows a checkerboard pattern starting with + at position (0,0).
+     *
+     * @return static A new matrix containing the cofactors.
+     */
+    public function cofactors(): static
+    {
+        return $this->getMatrixOfMinors()->applyAlternatingSigns();
+    }
+
     /**
      * Adds a MatrixInterface object to the current matrix and returns a new matrix with the sum.
      *

src/Samsara/Fermat/LinearAlgebra/Types/Traits/Matrix/ShapeTrait.php

@@ -30,11 +30,16 @@ public function getAdjoint(): static
     }
 
     /**
+     * Returns the adjugate matrix (also known as classical adjoint).
+     *
+     * The adjugate is the transpose of the cofactor matrix.
+     * This is different from getAdjoint() which is just the transpose.
+     *
      * @return static
      */
     public function getAdjugate(): static
     {
-        return $this->getAdjoint();
+        return $this->cofactors()->getAdjoint();
     }
 
     /**