Replace large matrix of complicated functions with simple symbols

Question

Given a matrix such as:

mat = {{0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, -((g m zg Cos[c] (j0 jz + jz^2 - 2 jz^2 Cos[c]^2 - j0 jz Cos[2 c] + jz^2 Cos[2 c]))/(-j0^2 jz - j0 jz^2 + 2 j0 jz^2 Cos[c]^2 + j0^2 jz Cos[2 c] - j0 jz^2 Cos[2 c])), 0, 0, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 0}};

$$\left( \begin{array}{cccccc} 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & -\frac{g m \text{zg} \cos (c) \left(-\text{j0} \text{jz} \cos (2 c)-2 \text{jz}^2 \cos ^2(c)+\text{jz}^2 \cos (2 c)+\text{j0} \text{jz}+\text{jz}^2\right)}{\text{j0}^2 \text{jz} \cos (2 c)+2 \text{j0} \text{jz}^2 \cos ^2(c)-\text{j0} \text{jz}^2 \cos (2 c)-\text{j0}^2 \text{jz}-\text{j0} \text{jz}^2} & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)$$

How would one replace the obvious large functional element with a generic latex symbol or simpler functional symbol such as f[a,b,c]

I need to compactly write large similar matrices with massive coupled functions similar to this, but many 1 or 0 elements which I would like to keep. I have naively tried:

mat /. Except[0 | 1, _?NumericQ] -> f[a,b,c]

Which simply replaced every single number and not the the entire functional. In the end I'm looking for:

$$\left( \begin{array}{cccccc} 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & f[a,b,c] & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)$$

Answer 1

Replace[mat, Except[0 | 1] -> f[a, b, c], {2}]

TeXForm @ %

$\left( \begin{array}{cccccc} 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & f(a,b,c) & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)$

Answer 2

mat =
  {{0, 1, 0, 0, 0, 0},
   {0, 0, 0, 0, 0, 0},
   {0, 0, 0, 1, 0, 0},
   {0, 0, -(g m zg Cos[c] (j0 jz + jz^2)), 0, 0, 0},
   {0, 0, 0, 0, 0, 1},
   {0, 0, 0, 0, 0, 0}};

---

Using MapAt:

p = Position[mat, x_ /; Head[x] =!= Integer, {2}, Heads -> False]

(*{{4, 3}}*)

MapAt[F[a, b, c] &, mat, p] // TeXForm

$\left( \begin{array}{cccccc} 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & F(a,b,c) & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)$

Answer 3

mat =
  {{0, 1, 0, 0, 0, 0},
   {0, 0, 0, 0, 0, 0},
   {0, 0, 0, 1, 0, 0},
   {0, 0, -(g m zg Cos[c] (j0 jz + jz^2)), 0, 0, 0},
   {0, 0, 0, 0, 0, 1},
   {0, 0, 0, 0, 0, 0}};

Using ReplaceAt (new in 13.1)

p = First @ Position[mat, x_ /; ! AtomQ[x], {2}]

{4, 3}

ReplaceAt[_ :> f[a, b, c], p] @ mat // MatrixForm