Jacobian Matrix

[thick imp]

am i getting it rightly .??

[gusty panther]

👋 Welcome to your Help Thread!

Hey @thick imp, Thanks for sharing your math problem with us. While you wait for a Helper to help you, we want to share some vital information with you.

●

Please take a moment to read the helpee guidelines. This will make sure that your post follows the helpee rules of our community.

●

Please don't ping <@&775784618955505685>, <@&1283689826742440016>, <@&819616364188139550>, or <@&624327278137966593> for help because their job is to take care of the server's administrative tasks, not to answer queries directly. However, if you have a problem with how a Helper is acting, you can ping a Helper Moderator.

●

It's always very useful if you can show us the work you've done so far. This makes it easier for our Helpers to find mistakes and help you get to the right answer.

Once you've got your answer and you're all set, you can close this thread by typing +close, and then you can click the Thank buttons to show your Helper some appreciation. · May 8, 2026, 5:46 AM

[gusty kayak]

what's your definition for the "jacobian" here? it seems to me that you are taking the derivative w.r.t. square matrices. This is not uncommon but we never called this jacobian.

[thick imp]

So I'm differentiating a matrix with respect to a matrix, where a matrix which is on the numerator side is something related to C is equals to A times B, where both A and B are the matrix product, sorry, where C is a matrix product of A and B. So I'm just differentiating it with respect to B. So is this a Jacobian or not?

C= A*B
dev(C)/dev(B) = 
is this a jacobian.??

[gusty kayak]

I don't get what you mean.

[thick imp]

ok let me go slow

[gusty kayak]

Making sense also works

A jacobian is usually concerned with derivatives of functions from Rn to Rm

not $\mathcal M_{m\times n}(\bR)\to\bR^k$

[pine cedar]

Coffey

[gusty kayak]

for those you should look into frechet derivatives.

[thick imp]

basically i am trying to understand backword auto grad
so i am facing this situation while evaluation of chain rule where
i am partially derivating a
state (assume it as C)
C = W2*(previous state)
dc/d(previous state)
previous state is w1*(input vec) +bias

[gusty kayak]

matrix calculus makes more sense given the context now

[thick imp]

is it clear.?? to you now.??

[gusty kayak]

not really no, idk what you want me to help with but read this wiki page : https://en.wikipedia.org/wiki/Matrix_calculus

[thick imp]

simply i wana know what actually a jacobian is i am not able to get the correct intuation

[gusty kayak]

A jacobian of a function at some point is the matrix of the linear map that approximates it well enough near that point

usually the denominators of jacobian are conventional vectors, not conventional matrices

[thick imp]

i see

[thick imp]

this is where i getting stucked
dev(v5)/dev(v4)

so my question is for this same partial derivative is this a jacobian.??

forget what i said previously

[thick imp]

,rotate

[thick imp]

,rotate

[thick imp]

,rotate

[gusty panther]

@thick imp

:HelpIcon:| Help Reminder

Hello ayandotjava, this is a friendly reminder that your help request has been inactive for more than 24 hours. If you no longer need assistance, please consider closing the thread using the +close command. This thread will be automatically closed in 3 days if it remains inactive.