Name:- Ashish Seth

Gate Score:- 632

Category:- OBC-NCL

Primary Subject:- Linear Algebra

My interview was conducted on 22-July-2020. It was an online interview which was conducted on google meet. My interview started at 10:33 am and went till 11:37 am.

Interviewers:- I1,I2,I3,I4

myself: M

I1: hello Ashish

M: Good Morning Sir..

I1: how are you Ashish

M: Sir little bit nerves…

I1:(Smiling) you Know Ashish there is a magical thing called Water. Kindly drink it you will feel better.

(Every professor present in the panel started laughing. Till then all my nervousness was gone)

I1: Ok Ashish introduce your self.

M: I tried to include as many point which i could think of in my introduction.

- college name and current SGPA
- current final year project
- how much i like linear algebra.

I1: you do know that it is not mandatory to do research on your selected primary subject but it is good that you like linear algebra because it is one the interviewer’s favorite subject.

I2:ok Ashish i think we can start off with a programming question. Write a function that take sorted int arr as a argument and return 1 or 0 to indicate the presence of duplicate.

M: It was easy for me so i did it in 1 min.

(than again I2 gave some modifiaction that were also simple)

I3: ok Ashish know we can switch to your primary subject.(He wrote a 4X4 permutation matrix(P) and a unknown matrix(U) and told me to do the product of two PU and UP)

M: Used column tech of multiplication for UP and row tech for PU.

I4: ok Ashish lets move on to next question do you no about rotation matrix and can you state 2X2 rotation matrix.

M: easly able to state and also told them some property like orthogonal matrix and rotation matrix will not change the l2 norm of a vector when multiplied.

I4 :(Next Question was kind of expected) prove how a rotation matrix will rotate any given vector.

M: prove with the help of dot product rule of two vector aTb.

I3:ok Ashish lets move on to next question. Lets say you have a Symm square matrix(A) do you know about its eigenvalues.

M: Sir they will be real.

I3: ok so now lets say we have a system define like this:

Ax=b than what about b ?

M: b must lie in the column space of A and its order will be nX1.

I3: ok so lets say you multiply A again and again to this system for m times where m is very large then what would happen.

M: i told him about symm matrix have complete set of eigen vectors so they are always diagonalizable. (we had about 10 min discussion regarding this fact where he gave me different rank matrices 1 to 3 and told me to check my statement on diff matrices). finally i was able to say that given eigen value of A being e, eigen value of A^2 will be e^2 and so on and the eigen vector will be same.

I3: ok ashish lets move on to next question given a matrix:

0.75 0.25

0.25 0.75 find its eigenvalues

M: (i was able to do it)

I3: Do you find anything special in this matrix.

M: Sir it is Symmetric and will have orthogonal eigen vector.

I3: Do you know about stotatic matrices:

M:(Never heard of it) No Sir.

I3: ok Ashish we are done from our side.

(After that i mentioned the interviewers about CS6015 course offered by iitm for Linear Algebra and how the Assignment and tutorials helped me).

**One of the best day of my life was 1 ^{st} Aug when result was declared and i found my name in MS(project) List.**