How to substitute curly brackets with round brackets in a grid of list

Question

I want to produce a table (or a grid) from my list of data, as follows:

eq01={0.01,1.02};
ev01={{1,3},{2,4}};
ev02={{5,5},{6,1}};
 data1 = {{"", "Equilibrium points", "Eigenvalues", 
   "Eigenvectors"}, {"A = 0",eq01,ev01,ev02}};

Grid[data1, Alignment -> Left, Spacings -> {2, 1}, Frame -> All, 
 ItemStyle -> "Text"]

And what I obtain is the following:

Is there a way to: 1) flatten the lists under "Eigenvalues" and "Eigenvectors" without using flatten for every definition of list in the beginning? Because I have many eigenvalues and eigenvectors and it would be very long; 2) substitute the curly brackets with round brackets, to have for example, in the second column and second row, (0.01,1.02)?

I hope the question is clear, thanks in advance!

Answer 1

Edit
this works exactly as OP asked in the comments below
also for many rows

eq01={0.01,1.02};
ev01={{1,3},{2,4}};
ev02={{5,5},{6,1}};
data1=StringReplace[#,{"{{"->"(","}}"->")","{"->"(","}"->")"}]&/@
ToString/@#&/@{{"","Equilibrium points","Eigenvalues","Eigenvectors"},{"A = 0",eq01,ev01,ev02}};

Grid[data1,Alignment->Left,Spacings->{2,1},Frame->All,ItemStyle->"Text"]

Answer 2

I think you have to use a custom formatting utility of some sort:

vectorForm[v_?VectorQ] := Row[{"(", Row[v, ","], ")"}];

Grid[data1 /. {
   m_?(MatrixQ[#, NumericQ] &) :> Row[vectorForm /@ m, ","], 
   v_?(VectorQ[#, NumericQ] &) :> vectorForm[v]},
 Alignment -> Left, Spacings -> {2, 1}, Frame -> All, 
 ItemStyle -> "Text"]

One distinct advantage of this approach is that it leverages Mathematica's expression formatting capabilities and avoids the lack of robustness of ToString[]. Compare the above method with @J42161217's on normalized eigenvectors:

eq01 = {0.01, 1.02};
ev01 = {{1, 3}, {2, 4}};
ev02 = Normalize /@ {{5, 5}, {6, 1}};

(* @MichaelE2 *)
data2 = {{"", "Equilibrium points", "Eigenvalues", 
    "Eigenvectors"}, {"A = 0", eq01, ev01, ev02}};
Grid[data2 /. {
   m_?(MatrixQ[#, NumericQ] &) :> Row[vectorForm /@ m, ","], 
   v_?(VectorQ[#, NumericQ] &) :> vectorForm[v]},
 Alignment -> Left, Spacings -> {2, 1}, Frame -> All, 
 ItemStyle -> "Text"]

(* @J42161217 *)
data2 = StringReplace[#, {"{{" -> "(", "}}" -> ")", "{" -> "(", 
        "}" -> ")"}] & /@ ToString /@ # & /@ {{"", 
     "Equilibrium points", "Eigenvalues", "Eigenvectors"}, {"A = 0", 
     eq01, ev01, ev02}};
Grid[data2, Alignment -> Left, Spacings -> {2, 1}, Frame -> All, 
 ItemStyle -> "Text"]

Something similar happens with ordinary fractions and square roots.

---

Original formatting, in which a set appears in set notation:

Grid[data1 /. v_?(VectorQ[#, NumericQ] &) :> vectorForm[v], 
 Alignment -> Left, Spacings -> {2, 1}, Frame -> All, 
 ItemStyle -> "Text"]

Answer 3

Another possibility is to define a form that automatically formats numeric vectors and numeric matrices as desired:

MakeBoxes[EigenForm[e_], StandardForm] ^:= Internal`InheritedBlock[
    {MakeBoxes},
    MakeBoxes[m_List?numericVectorQ, StandardForm] := RowBox[
        {"(", MakeBoxes[Row[m, ","], StandardForm], ")"}
    ];
    MakeBoxes[m_List?numericMatrixQ, StandardForm] := RowBox[
        BoxForm`AddCommas @ BoxForm`ListMakeBoxes[m, StandardForm]
    ];
    MakeBoxes[e, StandardForm]
]

SetAttributes[{numericMatrixQ, numericVectorQ}, HoldAll];

numericMatrixQ[e_]:=MatrixQ[Unevaluated[e], System`Dump`HeldNumericQ]
numericVectorQ[e_]:=VectorQ[Unevaluated[e], System`Dump`HeldNumericQ]

Michael's example:

eq01 = {0.01,1.02};
ev01 = {{1,3},{2,4}};
ev02 = Normalize/@{{5,5},{6,1}};

data2={{"","Equilibrium points","Eigenvalues","Eigenvectors"},{"A = 0",eq01,ev01,ev02}};
Grid[
    data2,
    Alignment -> Left, Spacings -> {2, 1}, Frame -> All, ItemStyle -> "Text"
] //EigenForm