Comparing Two Matrices: Same or Different?

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The discussion centers on comparing two matrices to determine if they are the same or different. The key point is that the interpretation of the operations represented by "^" and "\cdot" is crucial for understanding the matrices' equivalence. Without a clear definition of these operations, it is impossible to definitively conclude whether the matrices are identical. Participants emphasize the importance of context in mathematical notation. Clarifying these definitions is essential for accurate comparison.
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Are these the same thing?
http://upit.cc/i/4bf14079.png

...

and are these the same thing?
http://upit.cc/i/3ee58679.png

thanks everyone and god bless
~me
 
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That would depend upon exactly how "^" and "\cdot" are defined in your text.
 
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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