n=24
A= RandomReal[{-1,1},{n,n}];
A= A +Transpose[A];
A= A+ DiagonalMatrix[ RandomReal[{12, 23},{n}]];
MatrixPlot[A]
Eigenvalues[A]

Here be words. (∫_lower^upper)exprdvar

n=3;
A={{1.4,2,2.3},{1.2,3,-6.7},{1.2,1.2,-2.7}};
AInv=Inverse[A];
(* Comment *)
Norm[A.AInv - IdentityMatrix[n]]

A[[1]]
A[[1]]

αβχδϵϕγηιφκλμνωπθρστυ
𝔸𝔹𝔄𝒜  απ

AInv[[All,2]]
AInv[[{1,3}]]
AInv[[1,2]]
AInv[[All,1;;2]]

{n1,m1}={2,3};
{n2,m2}={4,2};
{n,m}={n1,m1}+{n2,m2};
A= RandomReal[ {0, 1}, {n,m}];
A11=A[[1;;n1,1;;m1]];
A12=A[[1;;n1,m1+1;;m]];
A22=A[[n1+1;;n,m1+1;;m]];
A21=A[[n1+1;;n,1;;m1]];
MatrixForm[A]
{
{MatrixForm[A11],MatrixForm[A12]},
{MatrixForm[A21],MatrixForm[A22]}
}
B= ArrayFlatten[ 
{
{A11,A12},
{A21,A22}
}
];
Norm[B-A]

n=4*1200;
A= RandomReal[{-1,1},{n,n}];
A= A+ Transpose[A];
b=RandomReal[{-1,1},n];
Timing[x=LinearSolve[A,b];]
Timing[ListPlot[Eigenvalues[A],
PlotRange->All]]
Norm[A.x -b]

MyCholeskyDecomposition[A_]:= Module[
{n=Length[A],R=0*A,i,j},
Do[
R[[i,i]]=(Sqrt[A[[i,i]]-Sum[((R[[k,i]])^2),{k,1,i-1}]]);
Do[
R[[i,j]]=(A[[i,j]]-Sum[R[[k,i]] R[[k,j]],{k,1,i-1}])/R[[i,i]],
{j,i+1,n}],
{i,1,n}];
R
]

n=4;
A= RandomReal[{-1,1},{n,n}];
A= A + Transpose[A];
A= A + DiagonalMatrix[RandomReal[{10,20},n]];
R= MyCholeskyDecomposition[A];
MmaR=CholeskyDecomposition[A];
Diagonal[A]
Norm[A- Transpose[R].R]

MmaR-R