Hermitian inner product

[rbeezer]

One patch adds the Hermitian inner product, by that name, for use with vectors over the complex numbers.

Second patch is totally doctests, no code changes. Explains, expands, and cross-references the dot product, inner product, Hermitian inner product and vector norm.

Depends on:

1. Add vector conjugation #10536

Apply:

1. attachment: trac_10683-hermitian_inner_product-v3.patch
2. attachment: trac_10683-vector-products-docs-v2.patch

Component: linear algebra

Author: Rob Beezer

Reviewer: Karl-Dieter Crisman

Merged: sage-4.7.alpha4

Issue created by migration from https://trac.sagemath.org/ticket/10683

[rbeezer]

Attachment: trac_10683-hermitian_inner_product.patch.gz

Attachment: trac_10683-vector-products-docs.patch.gz

[rbeezer]

comment:1

Apply patches in order given here:

Apply: trac_10683-hermitian_inner_product.patch

Apply: trac_10683-vector-products-docs.patch

[rbeezer]

Author: Rob Beezer

[rbeezer]

comment:2

Forgot: this depends on several patches, assuming 4.6.2.alpha0 or better (for #10364).

#10537, #10536 in that order, plus independently #10541

[rbeezer]

Attachment: trac_10683-hermitian_inner_product-v2.patch.gz

Apply first

[rbeezer]

Attachment: trac_10683-vector-products-docs-v2.patch.gz

Apply second

[rbeezer]

Description changed:

--- 
+++ 
@@ -1,3 +1,7 @@
 One patch adds the Hermitian inner product, by that name, for use with vectors over the complex numbers.
 
 Second patch is totally doctests, no code changes.  Explains, expands, and cross-references the dot product, inner product, Hermitian inner product and vector norm.
+
+Depends #10536
+
+Apply trac_10683-hermitian_inner_product-v2.patch, trac_10683-vector-products-docs-v2.patch

[rbeezer]

comment:3

After working with this for a while, I though it better to build off the dot product, rather than the inner product with its custom inner product matrices, due to the havoc that could result by specifying a matrix without the necessary properties for certain algorithms to run properly.

v2 series reflects this change. On 4.6.2.alpha4 depends only on #10536 now.