# Defining a function in terms of matrix elements

Currently trying to use elements from a matrix in defining a function however having some trouble. This is a somewhat simplified version of the problem.

Say I have the matrix

m={{Sin[x],Cos[x]},{Tan[x],ArcTan[x]}}


And I want to define a function in terms of the first element. How would I go about doing this ? Have tried

f[x_]:=m[[1,1,1]]


This seems to work until I try and evaluate it for a value of x.Then it just returns Sin[x].

Any help would be much appreciated.

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m = {{Sin[x], Cos[X]}, {Tan[x], ArcTan[x]}}; f[x_] := Evaluate@m[[1, 1]]; f[Pi] –  belisarius Jan 9 '14 at 17:15
Thanks, now got it working. Although I needed to use m[[1,1,1]] to get the first element from the matrix. m[[1,1]] returns the first row. –  user11642 Jan 9 '14 at 17:28
I now understand why. It is because I have it in matrix form. –  user11642 Jan 9 '14 at 17:35

## 2 Answers

You need to use Set instead of SetDelayed. Please see here for an explanation of the difference: What is the difference between Set and SetDelayed?

First make sure that x has no value assigned. Then you can do

In[1]:= m = {{Sin[x], Cos[x]}, {Tan[x], ArcTan[x]}}
Out[1]= {{Sin[x], Cos[x]}, {Tan[x], ArcTan[x]}}

In[2]:= f[x_] = m[[1, 1]]
Out[2]= Sin[x]

In[3]:= f[1]
Out[3]= Sin[1]

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One approach is this:

m = {{Sin[x], Cos[x]}, {Tan[x], ArcTan[x]}}
f[y_] := m[[1, 1]] /. x -> y

f[a]  -> Sin[a]


another:

m[x_] = {{Sin[x], Cos[x]}, {Tan[x], ArcTan[x]}}
f[y_] := m[y][[1, 1]]

f[b]  -> Sin[b]

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