works. We may write our initial vector as
Then
Since the eigenvalues with have
magnitude smaller than one, it follows that if and therefore , an eigenvector corresponding to the eigenvalue .
4. A Basic Diagram
5. SGML
Abbreviation for “Standard Generalized Markup Language”
International Standards Organization ISO 8879 [1986]
Principal Reference:
Charles F. Goldfarb, The SGML Handbook, Clarendon Press, Oxford, 1990.
6. Advantage of Using SGML
To mark up a document under an SGML document type
is to place it under a template for processing by
many different programs.
7. Transformations can be Chained
One form of processing is translation from one document
type to another. These transformations can be chained.
(Analogous to composition of functions.)
8. The Importance of Validation
For processing of an SGML document to be reliable the
document must be structurally correct.
To ensure structural correctness one may subject a document
to a validating parse.
When chaining transformations between SGML document types,
one should validate at each stage in order to protect the
integrity of the whole chained process.
9. XML Document Types
Every XML document type is canonically equivalent to an SGML
document type.
XML is essentially SGML with various restrictions.
Only XML document types should be served on the web.
(Classical HTML is an exception.)
There is substantially more software capable of handling XML
document types than is capable of handling typical SGML
document types that are not XML.
The XHTML + MathML version of these slides uses W3C's
Slidy by
Dave Raggett, a JavaScript/CSS package for sizing and flow control of
an HTML or XHTML slide show.
(The slides were generated in a non-standard fashion from GELLMU source.)
