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        wat do trace and rank of a matrix mean?????
7 years ago

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

All the best.
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Anil Pannikar
IIT Bombay


7 years ago
SAGAR SINGH - IIT DELHI
879 Points
										Dear unnati,
Let  be an  square matrix:

where

is the jth column vector and

is the ith row vector.
The n rows span the row space of  and the n columns span the column space of . The dimensions of these two spaces are the  same and called the rank of :

The determinant of  is denoted by

and we have

if and only if

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

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.

Sagar Singh
B.Tech, IIT Delhi


7 years ago
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