1 votes 1 votes x + y/2 = 9 3x + y = 10 The value of the Frobenius norm for the above system of equations is $0.5$ $0.75$ $1.5$ $2.0$ Linear Algebra gateit-2006 linear-algebra normal numerical-methods non-gate + – Ishrat Jahan asked Nov 1, 2014 • edited Jun 20, 2017 by Silpa Ishrat Jahan 1.5k views answer comment Share Follow See 1 comment See all 1 1 comment reply dragonball commented Apr 15, 2017 reply Follow Share @ Arjun Sir Is this in Gate Syllabus ? 1 votes 1 votes Please log in or register to add a comment.
1 votes 1 votes Answer: DFrobenius norm = $\sqrt{trace(A*A)}$ = 2.23 which is close to option D. Rajarshi Sarkar answered Apr 11, 2015 Rajarshi Sarkar comment Share Follow See all 4 Comments See all 4 4 Comments reply Sheshang commented Jun 3, 2016 i edited by Sheshang Dec 24, 2016 reply Follow Share if we take formula given by you, and count matrix as below: $\begin{bmatrix} 1 & 1/2 & 9\\ 3& 1& 10 \end{bmatrix}$ after that we have to fill third row of matrix by 0s to compute A*A, and this gives 2.23 as per your formula, but according to formula for Frobenius norm, following also allowable. $\sqrt{\sum \left | a_{ij} \right |^{2}}$ now if we take matrix as above, it gives answer = 13.86 and we take matrix as $\begin{bmatrix} 1 & 1/2 \\ 3& 1 \end{bmatrix}$ so it becomes √11.25 = 3.35 then which one is right? 1 votes 1 votes dragonball commented Apr 15, 2017 reply Follow Share How did u calculated ? 0 votes 0 votes Sheshang commented Apr 16, 2017 reply Follow Share i am also in confusion about formulae for frobenius norm. At various places, various formula are given for it. 1)The formula given by rajarshi sarkar is formula i found at multiple places. 2)Some references also site it as $\sqrt{trace(A*A^{T})}$ 3) While some references take $\sqrt{trace(A*A^{T})}$ as "reverse forbenius norm" and $\sqrt{trace(A^{T}*A)}$ as"forbenius norm". 4)The formula i used here $\sqrt{\sum \left |a _{ij} \right |^{2}}$ which i took from http://mathworld.wolfram.com/FrobeniusNorm.html Many other portals take this also as formula. 5)The last one i used with square matrix is just my doubt. As everywhere i saw that norm is calculated on square matrix. No one has ever discussed about what to do with equation-system, whether to include right side in matrix or not? So here i tried to put one more aspect that what about it? I am also in search of this answer, but this question went in dark corner and no exert has made comments on it, it is possible that it is out of course. But this what i have searched, i shared with you. 1 votes 1 votes dragonball commented Apr 16, 2017 reply Follow Share Thanks In gate 2017 paprer 1 there was a question based on forbenius norm. If u remember that eigen value question in set 1 gate 2017. 1 votes 1 votes Please log in or register to add a comment.