The LeadingPrincipalSubmatrix command returns the n-th leading principal submatrix of A.

The LeadingPrincipalSubmatrix is a special case of the LinearAlgebra[SubMatrix] command.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{NumericalAnalysis}\right]\right)\:$

$A≔\mathrm{Matrix}\left(\left[\left[1\,4\,7\,10\right]\,\left[4\,5\,8\,6\right]\,\left[7\,8\,10\,5\right]\,\left[5\,3\,5\,8\right]\right]\right)$

$A≔\left[\begin{array}{cccc}1& 4& 7& 10\\ 4& 5& 8& 6\\ 7& 8& 10& 5\\ 5& 3& 5& 8\end{array}\right]$

$\mathrm{LeadingPrincipalSubmatrix}\left(A\,3\right)$

$\left[\begin{array}{ccc}1& 4& 7\\ 4& 5& 8\\ 7& 8& 10\end{array}\right]$

$\mathrm{LeadingPrincipalSubmatrix}\left(A\,2\right)$

$\left[\begin{array}{cc}1& 4\\ 4& 5\end{array}\right]$

$\mathrm{LeadingPrincipalSubmatrix}\left(A\,1\right)$

$\left[\begin{array}{c}1\end{array}\right]$