Mathematica Tutorial

Getting and Setting Pieces of Matrices

m[[i,j]]	the i, j^th entry
m[[i]]	the i^th row
m[[All,i]]	the i^th column
Take[m,{i₀,i₁},{j₀,j₁}]	the submatrix with rows i₀ through i₁ and columns j₀ through j₁
m[[i₀;;i₁,j₀;;j₁]]	the submatrix with rows i₀ through i₁ and columns j₀ through j₁
m[[{i₁,...,i_r}, {j₁, ... , j_s}]]	the r×s submatrix with elements having row indices i_k and column indices j_k
Tr[m,List]	elements on the diagonal
ArrayRules[m]	positions of nonzero elements

Ways to get pieces of matrices.

Matrices in Mathematica are represented as lists of lists. You can use all the standard Mathematica list-manipulation operations on matrices.

Here is a sample 3×3 matrix.

This picks out the second row of the matrix.

Here is the second column of the matrix.

This picks out a submatrix.

m={{a₁₁,a₁₂,...},{a₂₁,a₂₂,...},...}	assign m to be a matrix
m[[i,j]]=a	reset element {i, j} to be a
m[[i]]=a	reset all elements in row i to be a
m[[i]]={a₁,a₂,...}	reset elements in row i to be {a₁, a₂, ...}
m[[i₀;;i₁]]={v₁,v₂,...}	reset rows i₀ through i₁ to be vectors {v₁, v₂, ...}
m[[All,j]]=a	reset all elements in column j to be a
m[[All,j]]={a₁,a₂,...}	reset elements in column j to be {a₁, a₂, ...}
m[[i₀;;i₁,j₀;;j₁]]={{a₁₁,a₁₂,...},{a₂₁,a₂₂,...},...}	reset the submatrix with rows i₀ through i₁ and columns j₀ through j₁ to new values