cell array of strings to matrix

Specific Case

For a simple specific case as listed in the question, you can use char to convert all the cell elements to characters and then subtract 96 from it, which is ascii equivalent of 'a'-1 -

A_numeric = char(A)-96

Sample run -

>> A
A = 
    'a'    'b'    'c'    'b'    'a'
>> A_numeric = char(A)-96
A_numeric =
     1
     2
     3
     2
     1

Generic Case

For a generic substitution case, you need to do a bit more of work like so -

%// Inputs
A = {'correct','boss','cat','boss','correct','cat'}
newcellval = {'correct','cat','boss'}
newnumval = [8,2,5]

[unqcell,~,idx]  = unique(A,'stable')
[~,newcell_idx,unqcell_idx] = intersect(newcellval,unqcell,'stable')
A_numeric = newnumval(changem(idx,newcell_idx,unqcell_idx))

Sample input-output -

>> A,newcellval,newnumval
A = 
    'correct'    'boss'    'cat'    'boss'    'correct'    'cat'
newcellval = 
    'correct'    'cat'    'boss'
newnumval =
     8     2     5
>> A_numeric
A_numeric =
     8     5     2     5     8     2

That's easy:

result = cell2mat(A)-'a'+1

For a generic association of letters to numbers 1,2,3...:

letters2numbers = 'abc'; %// 'a'->1, 'b'->2 etc.
[~, result] = ismember(cell2mat(A), letters2numbers)

For a generic association of strings to numbers 1,2,3...:

strings2numbers = {'hi', 'hello', 'hey', 'good morning', 'howdy'};
A = {'hello', 'hi', 'hello', 'howdy', 'bye'};
[~, result] = ismember(A, strings2numbers)

In this example,

result =
     2     1     2     5     0 

use a For Loop which iterate over A and convert character to number

for loop = 1:length(A)
  outMat(loop) = char(A(loop)) - 96
end

I hope it works.