Heat map + Numbers

First we write down the First Matrix, in which every number will be substituted by a color

N.B. The table contains also the Axis Legend.

  c1 = {
       {"Esol", "Ir", "Ru", "Sn", "Ti"}, 
       {"IrO2", 0.00, -0.14, 0.80, 0.37}, 
       {"RuO2", -0.10, 0.00, 1.03, 0.69}, 
       {"SnO2", 0.54, 0.43, 0.00, 0.17}, 
       {"TiO2", -0.71, 0.63, 0.62, 0.00}
       }

Second, we write down a Second Matrix, in which the numbers will be written over the colored tables

N.B. It's the same matrix as the first but limited to the numbers; The numbers ending with a zero have to be written between "", otherwise they will be rounded on the final figure (0.00 becomes 0.)

  c2 = {
       {"0.00", -0.14, "0.80", 0.37}, 
       {"-0.10", "0.00", 1.03, 0.69}, 
       {0.54, 0.43, "0.00", 0.17}, 
       {-0.71, 0.63, 0.62, "0.00"}
       }

Then we isolate the numerical part of the first matrix

  n1 = c1[ [2;;All,2;;All] ] 

And we assign the variables for the Colored table

  l1 = c1[ [2;;All,1] ] 
  p1 = c1[ [1,2;;All] ] 

Finally with the ImageCompose function, we overimpose the colored table to the numbered table

  ImageCompose[
     ArrayPlot[n1, ColorFunction -> "Rainbow", 
        ColorFunctionScaling -> True, Frame -> True, 
        FrameStyle -> Opacity[0], AspectRatio -> 0.737, 
        FrameTicks -> {{Transpose[{Range[Length[l1]], l1}], None}, {None, 
        Transpose[{Range[Length[p1]], p1}]}},
        FrameTicksStyle -> 
           Directive[Opacity[1], Bold, FontSize -> 60, FontFamily -> "Times"],
        Mesh -> All, MeshStyle -> White, ImageSize -> 1000],
     
     GraphicsGrid[c2, BaseStyle -> {"Times", 45, Bold, White}, 
        AspectRatio -> 0.75, ImageSize -> 780] , {580, 310}
     ]