How to prove that <x, A*Ax> > 0 ?

ot tl @Ot-Tl

18 August 2015 1 5K Report

Let H1, H2 be Hilbert spaces and

A : H1 → H2 be a compact operator with the singular

system (λn, vn, un).

How to prove that > 0 where denotes the inner product ?

Igor Vestfrid

By the definition of the adjoint operator, = = ||Ax||2. Thus, > 0 provided x does not belong to the kernel of A and it is zero otherwise.

Badges
Science topic

Similar topics
Social Science
Media
Journalism

More ot tl's questions See All

Can a differentiating mouse embryonic stem cell express ectoderm, mesoderm and endodem markers at the same time?

We are analysing the expression of Afp (endoderm marker), Sma (mesoderm) and Tuj1 (ectoderm) by mESCs that have been cultured in spontaneous differentiation conditions for 10 days with...

04 December 2022 7,507 1 View

Could someone help me identify these structures observed on spontaneously differentiating mouse embryonic stem cells in this SEM image?

We took an image of differentiating mESCs with SEM and observed these structures all over the cells in some regions of the coverslip. The structures are about 700 nm long. Any idea of what could...

02 November 2022 4,610 4 View

Which detection method is better for an ELISA-based assay: colorimetric or fluorometric?

Hello, I am planning to perform an ELISA-based assay to quantify the percentage of genomic methylation (5-methylcytosine) in human embryonic stem cells. I've been searching for some kits and I...

16 February 2021 8,716 3 View

Which is the best way to calculate doubling time for human embryonic stem cells?

Hi! I would like to perform a doubling time assay in several newly derived human embryonic stem cell lines. Since hESC must be passaged as cell clumps, I cannot know the exact number of cells I am...

10 February 2021 3,141 4 View

What's the most optimal design for a qPCR experiment with 10 samples and 16 genes?

Hi! I have to perform a qPCR experiment in which I would like to evaluate the expression of 13 genes (plus 3 HKG) on 10 samples. I must carry the runs on a 96-well qPCR plate since I need to...

14 November 2020 5,704 4 View

Who is the performer of flora of Uzbekistan?

Taxonomy and nomenclature of Poaceae. Very interesting and important project. Who is the performer of flora of Uzbekistan?

07 April 2019 7,558 4 View

The thermal expansion coefficient of Nickel, PMMA and glass. Any article or advice on this?

I am comparing between the of coeff of thermal expansion for Ni vs PMMA vs glass. Can anyone give an example of theses values?

17 March 2019 9,188 3 View

SU-8 soft baking and post exposure baking temperetures? What is the highest temperature can I used apart from 95c?

SU-8 soft baking and post exposure baking temperatures? What is the highest temperature can I use apart from 95C? I do not mean hard baking as I do not need this step for my application. Any...

15 March 2018 2,808 1 View

Can anyone tell me what should be the exposure time for SU-8 2002 and Omnicoat?

Can anyone tell me what should be the exposure time for SU-8 2002 and Omnicoat? I could not find it in the datasheet how many seconds or minutes

31 July 2017 420 2 View

How can I improve the performance of ZnO nanorods?

By cladding and what else can be done?

24 January 2017 1,666 2 View

How to learn more about SPSS and its Application?

I would like to learn more about SPSS and Its application especially in regards to data analysis. Please suggest me how I can learn more about it. Thank you so much.

11 August 2024 9,101 4 View

Can I base on reverse DNA sequences to perform alignment, convert to amino acids and GenBank submission?

I have reverse sequences (AB1 format), can I base on reverse DNA sequences to perform nucleotide alignment, convert nucleotides to amino acids and deposit the sequence in GenBank database?

11 August 2024 5,138 1 View

Baseline drift in HPLC? What causes this?

Hello, Why do i see this baseline drift when i compare my blank (black) to the sample (blue)? Any suggestions as to why this happened? Thank you!

11 August 2024 3,770 4 View

Text-Communication from the M1 Hand Area using BCI—and then there is Elon Musk?

Willett, Shenoy et al. (2021) have developed a brain computer interface (BCI) that used neural signal collected from the hand area of the motor cortex (area M1) of a paralyzed patient. The...

10 August 2024 7,180 0 View

Has anyone applied Python in the field of textile engineering for data analysis, automation, or smart textiles?

I'm currently exploring the application of Python in textile engineering, specifically in areas like data analysis, process automation, and the development of smart textiles. I'm interested in...

10 August 2024 7,429 2 View

How can I use the cif data obtained from rietveld refinement extracted via gsas2, for microstructural analysis using ETEX software?

09 August 2024 7,718 0 View

How are iso-frequency contours plotted?

Let's say we have a standard, regular hexagonal honeycomb with a 3-arm primitive unit cell (something like the figure attached; the figure is only representative and not drawn to scale). The...

07 August 2024 1,937 1 View

Is it possible to plot the atom-projected band structure using GPAW?

Hi, I'm currently working on a project where I need to plot the atom-projected band structure using GPAW. I've been able to calculate the band structure for my material, but I'm having trouble...

07 August 2024 269 3 View

How to prepare the nanoparticle treated fungal sample for Environmental SEM analysis?

A fungal strain was treated with nanoparticles. We want to do an environmental SEM analysis. So could anyone share your views on preparing the sample? Thank you.

07 August 2024 5,307 1 View

Should I include H atom into C3N5 when i am doing DFT modelling?

Hi all, my experimental XPS results shown that my C3N5 sample consists of N-H bond, hence in this case I should incorporate the N-H bond into my DFT modelling. However, I do notice several papers...

07 August 2024 8,414 2 View