MHB Invariance of Asymmetry under Orthogonal Transformation

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Orthogonal similarity transformation refers to a linear transformation that preserves angles and distances, typically represented by orthogonal matrices. The discussion emphasizes that the property of asymmetry remains unchanged when subjected to such transformations. Participants explore the mathematical proof of this invariance, highlighting the role of eigenvalues and eigenvectors in maintaining asymmetry. The conversation also touches on the implications of this property in various mathematical and physical contexts. Understanding orthogonal similarity transformations is crucial for grasping the concept of asymmetry invariance.
PkayGee
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Show that the property of asymmetry is invariant under orthogonal similarity transformation
 
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Okay, what IS an "orthogonal similarity transformation"? What is its definition? That's where I would start.
 
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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