MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
unnati dwivedi Grade: 12
        

wat do trace and rank of a matrix mean?????

7 years ago

Answers : (2)

Anil Pannikar AskiitiansExpert-IITB
85 Points
										

Dear Unnati,


 Trace : Sum of the elements of A (square matrix of order n ) lying along the principle diagonal is called trace of A.


Ex -   matrix =  1    0     so trace = 1+5 =6


                       0   5


Rank : No. r is said to be the rank of a m*n matrix A if,


1 every square sub matrix of order (r+1) or more is singular and


2 there exists at least one square submatrix of order r which is non singular


or rank of a matrix is the order of highest order non singular sub matrix


Ex - A = 1    2    3


            4    5    6


            3    4    5


we have det. A =0 so, r(A) is less then 3, also we have   5    6    a non singular square sub matrix of order 2 .


                                                                               4    5


hence rank of A = 2


 


 


Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation.


All the best.


Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.


Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar  respectively : Click here to download the toolbar..


 


Askiitians Expert


Anil Pannikar


IIT Bombay


 


 

7 years ago
SAGAR SINGH - IIT DELHI
879 Points
										

Dear unnati,


Let ${\bf A}$ be an $n \times n$ square matrix:


\begin{displaymath}{\bf A}=\left[ \begin{array}{cccc} a_{11} & a_{12} & \cdot &... ...n1} & a_{n2} & \cdot & a_{nn} \end{array} \right]_{n\times n} \end{displaymath}


where


\begin{displaymath}\left[ \begin{array}{c} a_{1j} a_{2j} ... a_{nj} \end{array}\right] \end{displaymath}


is the jth column vector and


\begin{displaymath}[a_{i1}\;a_{i2}\;\cdots\;a_{in}]\end{displaymath}


is the ith row vector.


The n rows span the row space of ${\bf A}$ and the n columns span the column space of ${\bf A}$. The dimensions of these two spaces are the same and called the rank of ${\bf A}$:


\begin{displaymath}R=rank({\bf A}) \leq N \end{displaymath}

 


The determinant of $A$ is denoted by


\begin{displaymath}det({\bf A}) = \vert {\bf A} \vert \end{displaymath}


and we have


\begin{displaymath}\vert {\bf A}{\bf B} \vert=\vert{\bf A}\vert\; \vert{\bf B}\vert \end{displaymath}

 



$rank({\bf A}) < N$ if and only if



$det({\bf A})=0$.


The trace of $A$ is defined as the sum of its diagonal elements:


\begin{displaymath}tr({\bf A}) = \sum_{i=1}^n a_{ii} \end{displaymath}









Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation.


All the best.


Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.


Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar  respectively : Click here to download the toolbar..


 


Askiitians Expert


Sagar Singh


B.Tech, IIT Delhi









7 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies
  • Complete AIPMT/AIIMS Course and Test Series
  • OFFERED PRICE: Rs. 15,900
  • View Details
  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: Rs. 15,900
  • View Details

Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details