Abstract Nonsense

Crushing one theorem at a time

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.

Continue reading

Advertisements

December 23, 2010 Posted by | Fun Problems, Halmos, Linear Algebra, Uncategorized | , , , , , , | Leave a comment

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


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

Continue reading

December 19, 2010 Posted by | Fun Problems, Halmos, Linear Algebra, Uncategorized | , , , , | 1 Comment

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.

Continue reading

December 19, 2010 Posted by | Fun Problems, Halmos, Linear Algebra, Uncategorized | , , , , , | 1 Comment

Halmos Section 36: Inverses (Pt. II)


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

Continue reading

December 3, 2010 Posted by | Fun Problems, Halmos, Linear Algebra, Uncategorized | , , , , , | 1 Comment

Halmos Section 36: Inverses (Pt. I)


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

Continue reading

December 2, 2010 Posted by | Fun Problems, Halmos, Linear Algebra, Uncategorized | , , , , , , | 1 Comment

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.

Continue reading

November 23, 2010 Posted by | Fun Problems, Halmos, Linear Algebra | , , , , , , , | 3 Comments

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.

Continue reading

November 22, 2010 Posted by | Fun Problems, Halmos, Linear Algebra, Uncategorized | , , , , | Leave a comment

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

Continue reading

November 18, 2010 Posted by | Fun Problems, Halmos, Linear Algebra, Uncategorized | , , , , , , , | Leave a comment

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.

Continue reading

November 8, 2010 Posted by | Fun Problems, Halmos, Linear Algebra, Uncategorized | , , , , , | Leave a comment

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.

Continue reading

October 27, 2010 Posted by | Fun Problems, Halmos, Linear Algebra | , , , , , | Leave a comment