## 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.

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

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

## 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.

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

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

## 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.

## 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.

## 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

## 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.

## 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.