Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![5.
Left and Right Inverses: We have only talked about inverses of square matrices.
This problem will explore the notion of a left and right inverse for a matrix that is not square. Let
To -1
A
1
0
=
1
a.
Compute AAT, (AAT)−¹ and AT (AAT)-¹. You may use inv() function and
matrix multplication in MATLAB or the Python equivalents (such as numpy.linalg.inv()).
b.
Show that the matrix B = AT (AAT)-¹ is a right inverse for A, i.e., verify that
AB= I. Is BA = I?
C.
Let A be a m × n matrix with m > n, and suppose that the n x n matrix AT A
is invertible. Suggest a formula of a left inverse C, i.e., find a matrix C such that CA = I. Your
expression for C should be in terms of A.
d.
Test formula of the left inverse from part (c) for the 2 x 1 matrix A
=
your
2
[3].](https://content.bartleby.com/qna-images/question/039207b8-632a-4dc4-a3c4-fd77b3c684b4/3c24691f-e470-4cba-b68d-e674a72bc931/4rgvvr_processed.png)
Transcribed Image Text:5.
Left and Right Inverses: We have only talked about inverses of square matrices.
This problem will explore the notion of a left and right inverse for a matrix that is not square. Let
To -1
A
1
0
=
1
a.
Compute AAT, (AAT)−¹ and AT (AAT)-¹. You may use inv() function and
matrix multplication in MATLAB or the Python equivalents (such as numpy.linalg.inv()).
b.
Show that the matrix B = AT (AAT)-¹ is a right inverse for A, i.e., verify that
AB= I. Is BA = I?
C.
Let A be a m × n matrix with m > n, and suppose that the n x n matrix AT A
is invertible. Suggest a formula of a left inverse C, i.e., find a matrix C such that CA = I. Your
expression for C should be in terms of A.
d.
Test formula of the left inverse from part (c) for the 2 x 1 matrix A
=
your
2
[3].
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