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How to calculate rank of 2 by 1 matrix..? 
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#1
Jan2213, 01:07 PM

P: 39

hey guys so i am well familiar with finding out rank of square matrices but if matrix is just a row or column vector then how to determine its rank..considering the example below:
a=[x1 x2 x3] where is column matrix while x1,x2,x3 are elements of this matrix..!! 


#2
Jan2213, 05:19 PM

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P: 11,617

Can you find the column rank (the number of independent columns)?
This is the same as the rank of the matrix. 


#3
Jan2213, 06:38 PM

P: 39

hi there
infact i am quite asking about how to calculate the rank of a column or row matrix..?? and here i have just taken the example of row matrix..but i would also like to know about determining rank of a column matrix..!! 


#4
Jan2313, 07:20 AM

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P: 39,348

How to calculate rank of 2 by 1 matrix..?
Any "n by 1" or "1 by n" matrix has rank "n".



#5
Jan2313, 09:10 AM

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P: 11,617




#6
Jan2313, 01:40 PM

P: 39




#7
Jan2313, 02:01 PM

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P: 11,617

It is not a different thing.
Can you find the column rank of a column matrix? It is easy, and the answer was already posted here. The same applies to a row matrix and the row rank. 


#8
Jan2413, 11:55 AM

P: 39

ok so can i say that any n by 1 or 1 by n matrix has rank of 1 ..!!
but what if the independent rows or row vectors and columns or column vectors have value more than 1 like i have an example as: x1=(1,3,4,2) x2=(3,5,2,2) x3=(2,1,3,2) so here i have three vetors x1,x2,x3 out of which two are independent x1,x2 while x3 is dependent as x3=(x1+x2)/2; and they all form a column matrix of 3 by 1 as A=[ x1 x2 x3 ] now acc to rule n by 1 and 1 by n we have rank 1 but checking independent rows as 2 so what should be rank 1 or 2..?? 


#9
Jan2413, 12:25 PM

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P: 11,617

2. I don't see any reason why you would expect 1. It is a 3x4matrix, this is neither nx1 nor 1xn.



#10
Jan2413, 01:21 PM

P: 39

now i am feeling stupid..!! i have been looking all along in terms of an individual vectors and not in terms of components ..!!
thanks..:) 


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