the way you described qn 8) is still unclear to me......i can suggest you to write the polynomial in taylor series form and ||p||k defined here satisfies all property of norm and then you can get option c) that is k>=d and NOT k>d because why should we should only with 0's it doesn't work that way.
Thank you so much for this explanation. I've a doubt sir. In last que opt 3 it is given that for all v in R^n. If we choose v=0 then we'll be getting q(x)=0 right? Is that means there is an eigenvalue equals to 0? If so, how can be det A is strictly greater than 0. Thank u in advance
Ax=0 iff x=0 how? Symmetric properties se solve hoga. (Ax,Ay) =(Ay ,Ax) We know (Ax,Ay) = (x,A^tAy) use for both sides we get AA^t=I So A is invertible
That i also know but in the given question they have not given that this is standard inner product(usual inner product) so we can not use this is always(bcz usual inner product is a part of inner product and every inner product is not usual hope you get my words)
Superb thanks alot sir...
Sir, can you please tell the 2 nd question obtain (b) how we can take the A matrix
Question no 14 take v1={√2/2,√2/2} v2={-√2/2,-√2/2} are unit vectors but not orthogonal to each other
In question 14 ||^2 =||v||^4 not square
In question 14. In expansion ||² =||v1||^4 because =||v||²
in the last question, is the matrix A defined on the standard inner product for V?
very good teaching....keep it up
Keep learning
the way you described qn 8) is still unclear to me......i can suggest you to write the polynomial in taylor series form and ||p||k defined here satisfies all property of norm and then you can get option c) that is k>=d and NOT k>d because why should we should only with 0's it doesn't work that way.
Thank you so much for this explanation. I've a doubt sir. In last que opt 3 it is given that for all v in R^n. If we choose v=0 then we'll be getting q(x)=0 right? Is that means there is an eigenvalue equals to 0?
If so, how can be det A is strictly greater than 0.
Thank u in advance
Very well explained sir ..it's really great helpful
Keep learning
Nice videos. Can you give lecture for abstract algebra, real and complex analysis
Real analysis and abstract algebra are available in our application
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@@mathematicalPathshala thank you sir
Well explained
Thanx,keep learning
Please start a full course for csir net
Thanku so much sir
Q no 13 is not correct explanation
Ohk give me the explanation where i am doing wrong
Ax=0 iff x=0 how?
Symmetric properties se solve hoga.
(Ax,Ay) =(Ay ,Ax)
We know (Ax,Ay) = (x,A^tAy) use for both sides we get AA^t=I
So A is invertible
Can u explain why (Ax,Ay)=(x,A^TAy)?
@@mathematicalPathshala (Ax,y) =(Ax)^t Y (for usual inner product)
=x^t A^t Y=(x,A^ty)
That i also know but in the given question they have not given that this is standard inner product(usual inner product) so we can not use this is always(bcz usual inner product is a part of inner product and every inner product is not usual hope you get my words)
Sir aapne part c ka que no. 66 solvve ni kiya
Is it from linear ?or functional?
@@mathematicalPathshala linear algebra
This is of topology not of linear
That we will cover in separate video of toplogy and metric spaces
Okk sir
In the last problem u said that = v^t Av. From where do get that ..
It comes from the matrix representation of inner product
Can you help me to know how inner product is expressed in terms of matrix....
Sir i want to join ur whatsap group..
Text on 8218203410
Explain in English sir.
Not good
Can you please tell us where we are not good?