Tagged Questions
3
votes
0answers
41 views
Tensor products over field do not commute with inverse limits?
In the question: Inverse limit of modules and tensor product, Matt E gives an example where inverse limits and tensor products do not commute over the base ring $\mathbb{Z}$. He then goes on to show ...
1
vote
1answer
51 views
Invariant Subspace Counterexample
Can someone give an example:
Suppose $T \in L(V)$. If $V = W \bigoplus W'$ and if $W$ is T-invariant then $W'$ is not necessarily T-invariant.
1
vote
1answer
260 views
Example of a Markov chain transition matrix that is not diagonalizable?
It is well-known that every detailed-balance Markov chain has a diagonalizable transition matrix. I am looking for an example of a Markov chain whose transition matrix is not diagonalizable. That is:
...
0
votes
0answers
34 views
What is the most motivating way of introducing the sketching of conics?
What is the most motivating way to introduce the sketching of conics which have a cross product terms?
This topic involves a lot of other stuff such as eigenvalues, orthogonal matrices, completing ...
4
votes
1answer
108 views
$A$ square matrix,nonsingular $\implies $ all submatrixes of $A$ are also nonsingular?
If a square matrix $A$ is nonsingular, then every submatrix of $A$ is also nonsingular.
I am trying to come up with a counter example. But most involve really difficult examples, so I am starting to ...
10
votes
1answer
81 views
Other Euler characteristics?
At the end of V.3.4 in Algebra: Chapter 0, Aluffi describes the construction of a Grothendieck group over the category of finite dimensional $\operatorname{k}$-vector spaces, ...
1
vote
3answers
140 views
5 linear equations in 5 unknowns
I need an example of 5 linearly independent equations with 5 variables. How can I write such a equation set. As an example:
...
9
votes
3answers
217 views
Deducing results in linear algebra from results in commutative algebra
Here are two examples of results which can be deduced from commutative algebra:
Any $n\times n$ complex matrix is conjugate to a Jordan canonical matrix (can be proven using the structure theorem ...
0
votes
1answer
163 views
Prove Axiom $10$ (Vector Spaces) independent of the others [duplicate]
Possible Duplicate:
Is it possible to construct a quasi-vectorial space without an identity element?
In Apostol Multivariable Calculus, $1.5$ exercise $30 b$, he asks the reader to prove ...
4
votes
2answers
113 views
The Duality Functor in Linear Algebra
I'm trying to gain an intuitive understanding of the following construction:
For any vector space $M$ over a field $R$, one can define the algebraic dual of $M$ as $M^* := \mathsf{Hom}(M, R)$ and ...
1
vote
2answers
166 views
Example of eigenvectors in different bases (follow-up question)
This is a follow-up question on this one: Connection between eigenvalues and eigenvectors of a matrix in different bases
Assume I have matrix
$$
B=\left(
\begin{array}{cccc}
0 & 0 & 1 ...
5
votes
2answers
1k views
Examples for proof of geometric vs. algebraic multiplicity
Here you see a supposedly easy proof of a well-known theorem in linear algebra:
Although I know I should understand this, I don't :-(
Obviously there are too many indices and stuff, so I don't see ...
9
votes
6answers
2k views
How are eigenvectors/eigenvalues and differential equations connected?
In school and at university we never had eigenvalues nor differential equations, so these concepts were really giving me a hard time. Now I developed some intuition for both concepts.
I learned that ...
2
votes
2answers
303 views
Tips for writing math solutions for others
I am working a bit on a collection of Linear Algebra examples,
as well as some examples on induction. This is what is taught freshman year at our university.
I intend to release this to the public, ...
