Matrix transformation notation

Question

I have a question about a transformation of a matrix. Lets say we have the following matrix

$ M = \left[ {\begin{array}{cc} 4 & 3 \\ 4 & 3 \\ \end{array} } \right] $

Then I want to transform all numbers in the matrix with the following function:

$f(x) = (x - 4)^2 + 2x -4$

What would be the correct notation for this?

Answer 1

Maybe I don't understand your question, but: what's wrong with this?

$$ \begin{pmatrix} f(4) & f(3) \\\ f(4) & f(3) \end{pmatrix} $$

More generally, if you have a matrix $(a^i_j)$, you could write the resulting matrix as $(f(a^i_j))$.

Answer 2

Could use the "Hadamard Product"... I don't know whether there is a consistently accepted notation for such a product, however a few examples here and on Wikipedia seem to use an open circle.

In that sense, your expression would take the form

$(M-4O)\circ(M-4O)+2M-4O$ where $O= \left( \begin{array} {cc} 1 &1 \\ 1&1 \end{array} \right) $

In MATLAB, use .* for element-wise multiplication.

There are probably other possibilities.