Merge pull request #552 from martinjaggi/master. Closes #552.

tex formulas in the documentation

using mathjax.
and spliting the MLlib documentation by techniques

see jira
https://spark-project.atlassian.net/browse/MLLIB-19
and
https://github.com/shivaram/spark/compare/mathjax

Author: Martin Jaggi <m.jaggi@gmail.com>

== Merge branch commits ==

commit 0364bfabbfc347f917216057a20c39b631842481
Author: Martin Jaggi <m.jaggi@gmail.com>
Date:   Fri Feb 7 03:19:38 2014 +0100

    minor polishing, as suggested by @pwendell

commit dcd2142c164b2f602bf472bb152ad55bae82d31a
Author: Martin Jaggi <m.jaggi@gmail.com>
Date:   Thu Feb 6 18:04:26 2014 +0100

    enabling inline latex formulas with $.$

    same mathjax configuration as used in math.stackexchange.com

    sample usage in the linear algebra (SVD) documentation

commit bbafafd2b497a5acaa03a140bb9de1fbb7d67ffa
Author: Martin Jaggi <m.jaggi@gmail.com>
Date:   Thu Feb 6 17:31:29 2014 +0100

    split MLlib documentation by techniques

    and linked from the main mllib-guide.md site

commit d1c5212b93c67436543c2d8ddbbf610fdf0a26eb
Author: Martin Jaggi <m.jaggi@gmail.com>
Date:   Thu Feb 6 16:59:43 2014 +0100

    enable mathjax formula in the .md documentation files

    code by @shivaram

commit d73948db0d9bc36296054e79fec5b1a657b4eab4
Author: Martin Jaggi <m.jaggi@gmail.com>
Date:   Thu Feb 6 16:57:23 2014 +0100

    minor update on how to compile the documentation

1 files changed, 61 insertions, 0 deletions

diff --git a/docs/mllib-linear-algebra.md b/docs/mllib-linear-algebra.md
new file mode 100644
index 0000000000..cc203d833d
--- /dev/null
+++ b/docs/mllib-linear-algebra.md
@@ -0,0 +1,61 @@
+---
+layout: global
+title: MLlib - Linear Algebra
+---
+
+* Table of contents
+{:toc}
+
+
+# Singular Value Decomposition
+Singular Value `Decomposition` for Tall and Skinny matrices.
+Given an `$m \times n$` matrix `$A$`, we can compute matrices `$U,S,V$` such that
+
+`\[
+ A = U \cdot S \cdot V^T
+ \]`
+
+There is no restriction on m, but we require n^2 doubles to
+fit in memory locally on one machine.
+Further, n should be less than m.
+
+The decomposition is computed by first computing `$A^TA = V S^2 V^T$`,
+computing SVD locally on that (since `$n \times n$` is small),
+from which we recover `$S$` and `$V$`.
+Then we compute U via easy matrix multiplication
+as `$U =  A \cdot V \cdot S^{-1}$`.
+
+Only singular vectors associated with largest k singular values
+are recovered. If there are k
+such values, then the dimensions of the return will be:
+
+* `$S$` is `$k \times k$` and diagonal, holding the singular values on diagonal.
+* `$U$` is `$m \times k$` and satisfies `$U^T U = \mathop{eye}(k)$`.
+* `$V$` is `$n \times k$` and satisfies `$V^T V = \mathop{eye}(k)$`.
+
+All input and output is expected in sparse matrix format, 0-indexed
+as tuples of the form ((i,j),value) all in
+SparseMatrix RDDs. Below is example usage.
+
+{% highlight scala %}
+
+import org.apache.spark.SparkContext
+import org.apache.spark.mllib.linalg.SVD
+import org.apache.spark.mllib.linalg.SparseMatrix
+import org.apache.spark.mllib.linalg.MatrixEntry
+
+// Load and parse the data file
+val data = sc.textFile("mllib/data/als/test.data").map { line =>
+  val parts = line.split(',')
+  MatrixEntry(parts(0).toInt, parts(1).toInt, parts(2).toDouble)
+}
+val m = 4
+val n = 4
+val k = 1
+
+// recover largest singular vector
+val decomposed = SVD.sparseSVD(SparseMatrix(data, m, n), k)
+val = decomposed.S.data
+
+println("singular values = " + s.toArray.mkString)
+{% endhighlight %}