Inverse of Matrix Sum Formula: Solving for Upper Triangular Matrices

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The discussion centers on finding a formula for the inverse of the sum of two upper triangular matrices. Participants question the existence of such a formula and suggest examining specific examples of upper triangular matrices. The inquiry includes a detailed look at the sum of two matrices in the form of a 2x2 upper triangular structure. The conversation highlights the complexity of deriving an inverse in this context. Ultimately, the need for a clear formula remains unresolved.
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Does anyone know a formula for the inverse of a sum of two upper triangular matrices?
 
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What makes you think there is such a formula?

Have you looked at the inverse of
\left(\begin{array}{cc}a & b \\ 0 & c\end{array}\right)+ \left(\begin{array}{cc}x & y \\ 0 & z\end{array}\right)?
 
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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