Let A be a square matrix. If the mapping Ax^+ is Minty-Browder monotone, then A is positive semidefinite. Is the converse true?

07 July 2016 1 5K Report

x=(x_1,...,x_n)^T, x^+=(max(x_1,0),...,max(x_n,0)), A has n lines and Ax^+ means A multiplied by x^+. Everything is real.

Sándor Zoltán Németh

It seems is not true. Take A=[1 1;0 1], x_1=-3, y_1=-1, x_2=2 and y_2=1. Let me modify the question:

When is Ax^+ Minty-Browder monotone?

Badges
Science topic

Similar topics
Mathematics
Algebra
Matrix

More Sándor Zoltán Németh's questions See All

Which results are more important in mathematics, the ones with an immediate impact (few years) or the ones with a delayed impact (several decades)?

Should we always try to achieve immediate impact for our results? How to decide if a result is promising (that is, it will be important several decades later) or not? Can a mathematical result...

08 September 2015 2,555 4 View

Does anybody know about "true" applications of cone-complementarity problems where the cone is essentially different from the nonnegative orthant?

I consider an application a "true" one if it does not come as a reformulation of an optimization problem. I already know about applications of the second order and positive semidefinite...

05 June 2015 3,335 4 View

I think isotonic regression should be important in finance. Does anybody know about any applications of isotonic regression in finance?

My feeling is based on the following idea: Expected behaviour of financial data could have ordering properties. For example one may expect the increase in price of some stock in a given time...

05 June 2015 3,483 4 View

How to classify strictly upper triangular matrices by similarity?

Let F be a field. Consider U, the set of n times n strictly upper triangular matrices in F. For X, Y in U, we call them similar if there exists some S, which is non-degenerate and upper...

01 March 2021 2,957 8 View

Is CD44 degraded in lysosome together with hyaluronan after CD44 mediated endocytosis of hyaluronic acid?

Also when RHAMM binds hyaluronic acid, they get internalized, will RHAMM also be degraded? Or both CD44 and RHAMM will be transferred back to the cell membrane? Asking for breast cancer cell line...

01 March 2021 8,169 2 View

Why is the sum of the elements in a row in a Q matrix equal to zero?

When explaining substitution models, the substitutions are expressed as Q matrix. Why is the sum of the elements in a row zero?

28 February 2021 3,864 3 View

Distribution of particles in metal matrix?

How would define the "good" and "poor" distribution of particles within the matrix. Is there a quantitative solution to assess the distribution of the particles, which then having denotation of...

28 February 2021 7,397 8 View

How to find a correlation between coordinates in a curvilinear coordinate system?

Hello. I have a skewed elliptical coordinate system (I use alternative elliptical coordinates). And I need to determine connections between coordinates in order to fetch a covariance matrix of...

28 February 2021 364 3 View

For modelling epoxy-based matrices (in composites), which model in ABAQUS is the most suitable, Concrete damaged plasticity or Drucker-Prager model?

I am working on developing a micromechanical FE model for predicting kink-band formation in UD composites. To model matrix plasticity, which model, out of Concrete Damaged Plasticity and...

28 February 2021 5,415 1 View

How do I choose contrasts in SPM8?

I am learning how to use SPM for PET and PET-MR analysis, but I haven't found any great resources that explain how contrasts work. I have a series of PET images where our hypothesis argues that...

24 February 2021 1,534 2 View

What are the methods used for CNT..?

Respected Professor's i hope you are doing well and happy. i need some information about carbon Nanotubes. before blending the CNT with the matrix the CNT has been introducing in some treatments....

24 February 2021 5,383 5 View

How can I generate random samples from Bingham distribution in R? How can I construct those symmetric matrices?

in the function rbingham(n,A) in R software how can I construct that A (symmetric) matrix?

24 February 2021 3,528 3 View

How does the injection volume impact LLOQ and ULOQ in regression analysis (LC-MSMS)?

Hello, I have run into an issue that has sparkled a debate at work: is the LLOQ/ULOQ impacted by injection volume under the following circumstances: 1) Same dilution factor of all samples 2)...

23 February 2021 9,159 3 View