Book Image

Sage Beginner's Guide

By : Craig Finch
1 (1)
Book Image

Sage Beginner's Guide

1 (1)
By: Craig Finch

Overview of this book

Table of Contents (17 chapters)
Sage Beginner's Guide
Credits
About the Author
About the Reviewers
www.PacktPub.com
Preface
Index

Time for action – trying other matrix methods


Let's test out some other methods of the Matrix object:

A = matrix(QQ, [[2, 5, 4], [3, 1, 2], [5, 4, 6]])
print("Matrix A:")
show(A)

# Scalar operations
print("Determinant of A: {0}".format(A.det()))
print("Rank of A: {0}".format(A.rank()))
print("Euclidean norm: {0}".format(A.norm()))
print("Frobenius norm: {0}".format(A.norm('frob')))

# Matrix operations
print("Transpose of A:")
show(A.transpose())
print("Inverse of A:")
show(A.inverse())
print("Adjoint of A:")
show(A.adjoint())
print("Testing adj(A)/det(A) == inverse(A)")
A.adjoint()/A.det() == A.inverse()

The output should look like this:

What just happened?

We created an object that represents a 3 by 3 matrix of rational numbers, and used its methods to calculate the determinant and rank of A. We then calculated its inverse and its adjoint, and verified the relationship between them. We also used the norm method to compute two different norms of the matrix. When called with no arguments...