
Linear Algebra Linear Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
May 15th, 2016, 07:59 AM  #1 
Newbie Joined: May 2016 From: London Posts: 1 Thanks: 0  Relationship between a rank and the limit of a matrix
So I have a question, Let's suppose I have a matrix $M$, where all the elements $a_{ij}$ are linear expressions that are functions of an arbitrary number of variables i.e. $$a_{ij}=f_{ij}(x_{1},x_{2},...,x_{n})$$ Let's suppose that I take the limit of one of these variables to infinity i.e. Take $x_{1}\rightarrow\infty$ and call the resulting matrix $M_{x_{1}\rightarrow\infty}$ My question is are the ranks of these two matrices related? Put in other words Is $rank(M)$ related to $rank(M_{x_{1}\rightarrow\infty})$ Does anyone know the answer to this question or know of a text/source that does have the answer? Thank you 
May 22nd, 2016, 01:57 AM  #2 
Senior Member Joined: Aug 2012 Posts: 229 Thanks: 3 
Hey AdemH. If your function is indeed a linear one then the matrix itself should remain static. You usually apply an operator (including a matrix) to a vector of values and evaluate it. The matrix and its properties are usually static and therefore don't change even if the mapping does as a function of its inputs. 

Tags 
limit, matrix, rank, relationship 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Rank of a matrix  MATHEMATICIAN  Linear Algebra  4  March 8th, 2016 11:43 AM 
rank of matrix  Bhuvaneshnick  Algebra  0  December 22nd, 2014 11:37 PM 
Rank of a matrix with a parameter  costarea  Algebra  1  November 1st, 2014 01:12 PM 
The Rank of a matrix  fahad nasir  Linear Algebra  10  July 26th, 2013 10:22 AM 
matrix rank  waytogo  Linear Algebra  1  June 14th, 2012 11:56 AM 