I am interested with Map and Reduce operations in computer science. I would like to do analogies with Mathematics and especially with Linear Algebra. ReduceFirst, could we say that Reduce operation can be translated as a linear form, ie I start from a vector and I get a scalar from the coordinates of the initial vector ? But a linear form is by definition linear, is it always the case for Reduction in computer science ?MapSecondly, could we say that Map can be translated as an endomorphism, i.e we start from an initial vector (like a list in computer science) and we get also a vector as output.If I take Map operation, and f a function, I have :$f[x_{1}, x_{2} ..., x_{n}] = [ f(x_{1}), f(x_{2}), ..., f(x_{n})]$I could write it like this :$f[\vec{X}] = f [\sum_{i=1}^{n}\,x_{i}\,\vec{e_{i}}]= \sum_{i=1}^{n}\,x_{i}\,\vec{f(e_{i})}=\sum_{i=1}^{n}\,x_{i}\,F_{ij}\,\vec{e_{j}}=[f(x_{1}), f(x_{2}), ..., f(x_{n})]$So I get : $f(x_{j})=\sum_{i=1}^{n}\,F_{ij}\,x_{i}$ with $F_{ij}$ called the matrix of change basis of the endomorphism f But I don't get this relation above, well known between a change of basis (Matrix $F_{ij}$) and coordinates into 2 basis :$x_{j} = F_{ij}\,x'_{i}$I don't know how to make correct connections between Linear algebra and Map,Reduce operations ?If someone could help to Conceptualize these operations, this would be nice.ThanksPS: don't hesitate to transfer this question to mathematics exchange community if necessary.
Connections between Map Reduce operations and Linear Algebra
algorithms