What does the multiplication of matrix represents?

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    Matrix Multiplication
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Matrix multiplication represents the consecutive application of two linear transformations, as indicated by the matrices involved. Each matrix functions as a mapping that takes a vector as input and produces another vector as output. This process can be viewed as the composition of the functions represented by the matrices, facilitating transformations between different vector spaces. Understanding this concept is crucial for grasping advanced topics in linear algebra and its applications.

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As we know that 2×3 = 2+2+2 = 6;
so similarly what does matrix multiplication represents?
 
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parshyaa said:
As we know that 2×3 = 2+2+2 = 6;
so similarly what does matrix multiplication represents?
It means the consecutive application of two linear transformations represented by the matrices.
 
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Here's another explanation. A matrix can be thought of as a kind of function, one that takes a vector as its input, and produces another vector as its output. Multiplication of two matrices is equivalent to the composition of the functions that are represented by the matrices. I've explained this in terms of functions, but the usual terminology is linear transformations, mappings between vectors in one space to vectors in possibly a different space.
 
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