Grassmann Algebra

ExplorGrassmannMatrixAlgebra.nb 26
� Solving matrix equations
Here we take an example and show that GrassmannLeftLinearSolve and
GrassmannRightLinearSolve both gives solutions to a matrix exterior equation.
M � ��1 � x, x � y�, �1 � y, 2 � y � x � 5�x � y��; MatrixForm�M�
1 � x x�y �
1 � y 2�x�y � 5x� y �
Y � �3 � 2x� y, 7 � 5�x�; MatrixForm�Y�
�
3 � 2x� y
7 � 5x �
GrassmannLeftLinearSolve gives:
X � GrassmannLeftLinearSolve�M, Y�; MatrixForm�X�
����
�
3 � 3x
2 � 2x� y
��� � 2
����M � X�� � Y
True
19 x�y
����������� 4
����
�
GrassmannRightLinearSolve gives:
X � GrassmannRightLinearSolve�M, Y�; MatrixForm�X�
�����
�
2001 4 26
� 1 ��� � 2
7
��� 2 �
19 x 21 y 41 x�y
�������� � �������� � �����������
4 4 4
17 x 7y 29 x�y
�������� 4 � ������ 4 � ����������� 4
����X � M�� � Y
True
�����
�