MHB Matrix Rank: Real-Life Applications & Motivation

matqkks
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Are there any real life applications of the rank of a matrix? It need to have a real impact which motivates students why they should learn about rank.
 
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matqkks said:
Are there any real life applications of the rank of a matrix? It need to have a real impact which motivates students why they should learn about rank.

Hi matqkks, :)

The concept of rank of a matrix has applications in control theory as described here. And I think you can find countless number of applications of control theory. Here is a video I found that you may be interested in,



Kind Regards,
Sudharaka.
 
Thread 'How to define a vector field?'

Thread 'How to define a vector field?'

Hello! In one book I saw that function ##V## of 3 variables ##V_x, V_y, V_z## (vector field in 3D) can be decomposed in a Taylor series without higher-order terms (partial derivative of second power and higher) at point ##(0,0,0)## such way: I think so: higher-order terms can be neglected because partial derivative of second power and higher are equal to 0. Is this true? And how to define vector field correctly for this case? (In the book I found nothing and my attempt was wrong...
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