High School What are matrix transformations?

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Matrix transformations refer to the linear mappings between finite-dimensional vector spaces, often used to model geometric operations like rotations and reflections. A matrix essentially represents a transformation, which is a key concept in understanding its applications. Clarification may be needed on whether the discussion pertains to the linear transformation defined by the matrix or the process of changing the matrix itself, such as through a change of bases. Understanding these distinctions is crucial to avoid confusion in the topic. Overall, matrix transformations play a significant role in various mathematical and applied contexts.
Sreekar adithya
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TL;DR
Quick understanding of transformation of an matrix
What does a transformation of a matrix means and how it could be used?
 
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A matrix corresponds to a linear mapping between (finite dimensional) vector spaces. It can for example be used to model rotations or reflections. Here is a video that explains it better than I ever could:

 
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Like QED said, repeating because I think it is an important point in avoiding confusion. A matrix describes or represents a transformation, that is what is usually meant by a matrix transformation.
 
we might need more info from the OP, as to whether he means the linear transformation defined by the matrix, or the transformation of the matrix, i.e.changing it to some other matrix, defined by a change of bases, say.
 
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Thread 'Confusion about the Moyal-Weyl twist'

I am studying the mathematical formalism behind non-commutative geometry approach to quantum gravity. I was reading about Hopf algebras and their Drinfeld twist with a specific example of the Moyal-Weyl twist defined as F=exp(-iλ/2θ^(μν)∂_μ⊗∂_ν) where λ is a constant parametar and θ antisymmetric constant tensor. {∂_μ} is the basis of the tangent vector space over the underlying spacetime Now, from my understanding the enveloping algebra which appears in the definition of the Hopf algebra...
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