# Abstract Nonsense

## Halmos Sections 39 and 40: Invariance and Reducibility

Point of post: In this post we complete the problems at the end of sections 39 and 40 in Halmos.

December 23, 2010

## Halmos Sections 37 and 38: Matrices and Matrices of Linear Transformations(Pt. II)

Point of post: This is a continuation of this post.

December 19, 2010

## Halmos Sections 37 and 38: Matrices and Matrices of Linear Transformations(Pt. I)

Point of post: In this post I will complete the problems listed at the end of sections 37 and 38 of Halmos.

Remark: For those who are just interested in the solutions to Halmos and haven’t read my side-along postings you will probably need to see the series of posts for which this and this are the first posts for notation.

December 19, 2010

## Halmos Section 36: Inverses (Pt. II)

Point of post: This is a continuation of this post.

December 3, 2010

## Halmos Section 36: Inverses (Pt. I)

Point of post: In this post we complete the problems at the end of section 36 in Halmos.

December 2, 2010

## Halmos Sections 34 and 35:Products and Polynomials

Point of post: In this post we complete the problems at the end of sections 34 and 35 of Halmos’s book.

November 23, 2010

## Halmos Sections 32 and 33: Linear Transformations and Transformations as Vectors (Pt. II)

Point of post: This is a continuation of this post in an effort to answer the questions at the end of sections 32 and 33 in Halmos’s book.

November 22, 2010

## Halmos Section 29,30 and 31: Multilinear Forms, Alternating Multilinear Forms, Alternating Multilinear Forms of Maximal Degree

Point of post: In this post we solve the problems given at the end of the sections 29,30 and 31 in Halmos’s book

November 18, 2010

## Halmos Section 26 and 27: Permutations and Cycles

Point of post: In this post we’ll complete the problems in chapters 26 and 27 of Halmos’s book.

November 8, 2010

## Halmos Section 23: Bilinear Forms

Point of post: This post will document the solutions to Halmos’s section 23 on Bilinear forms, the content of which is explained (not quoted) here. Some interesting results in this post is the, very very perfunctory, discussion of quadratic forms and a how a symmetric bilinear form on a field of characteristic greater than two is completely determined by it’s associated quadratic form.

Remark: As usual, I use somewhat different notation than Halmos. To see this, and examples, etc. see the above link.

October 27, 2010