Skip to main content Accessibility help
×
Hostname: page-component-5c6d5d7d68-wpx84 Total loading time: 0 Render date: 2024-08-17T00:07:41.345Z Has data issue: false hasContentIssue false

8 - Fundamental Subspaces of S

from PART II - MATHEMATICAL REPRESENTATION OF RECONSTRUCTED NETWORKS

Published online by Cambridge University Press:  05 September 2012

Bernhard Ø. Palsson
Affiliation:
University of California, San Diego
Get access

Summary

In the last chapter we discussed the elementary topological properties of the network that the stoichiometric matrix represents. In this chapter we look deeper into the properties of the stoichiometric matrix and how these fundamental topological properties can be used to obtain a more thorough understanding of the reaction network that it represents. This material is perhaps the most mathematical part of this book. It should be readily accessible to readers with formal education in the physical and engineering sciences, while readers with a life science background may find it challenging. The concepts introduced are important to the rest of the chapters in Part II. The stoichiometric matrix is a mathematical mapping operation (recall Figure 6.1). Matrices have certain fundamental properties that describe this mapping operation. These properties are contained in the four fundamental subspaces associated with a matrix. This chapter discusses these subspaces and how we can mathematically define them and interpret their contents in biochemical and biological terms.

Dimensions of the Fundamental Subspaces

The mapping that the stoichiometric matrix represents was illustrated in Figure 6.1 and a preliminary discussion of the associated four subspaces is found in Chapter 6. The stoichiometric matrix is typically rank deficient. The rank r of a matrix denotes the number of linearly independent rows and columns that the matrix contains. Rows are linearly dependent if any one row can be computed as a linear combination of the other rows.

Type
Chapter
Information
Systems Biology
Properties of Reconstructed Networks
, pp. 118 - 135
Publisher: Cambridge University Press
Print publication year: 2006

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×