Upgrading from:

LinearAlgebra`MatrixManipulation`

AppendColumns, AppendRows, and BlockMatrix are available using the Mathematica kernel functions Join and ArrayFlatten.
TakeRows, TakeColumns, TakeMatrix, and SubMatrix are available using the Mathematica kernel function Take.
HankelMatrix and HilbertMatrix are available as the kernel functions HankelMatrix and HilbertMatrix.
The functionality of ZeroMatrix can be obtained using the new kernel function ConstantArray.
The functionality of PolarDecomposition can be obtained using the enhanced Mathematica kernel function SingularValueDecomposition.
MatrixPlot is now available as the kernel function MatrixPlot.

Join two matrices:

Version 5.2 << LinearAlgebra`MatrixManipulation`; A = Array[a, {2, 2}]; B = Array[b, {2, 2}]; AppendRows[A, B] // MatrixForm

Create a block matrix from submatrices:

Version 5.2 << LinearAlgebra`MatrixManipulation`; A = Array[a, {2, 2}]; B = Array[b, {2, 2}]; BlockMatrix[{{A, B}, {B, {{0, 0}, {0, 0}}}}] // MatrixForm

Pick out a submatrix:

Version 5.2 << LinearAlgebra`MatrixManipulation`; TakeMatrix[Array[a, {5, 5}], {2, 2}, {3, 4}] // MatrixForm

Create special type matrices:

Version 5.2 << LinearAlgebra`MatrixManipulation`; HankelMatrix[3] // MatrixForm
Version 5.2 << LinearAlgebra`MatrixManipulation`; HilbertMatrix[3] // MatrixForm

LowerDiagonalMatrix, UpperDiagonalMatrix, and TridiagonalMatrix can be replaced by the following definitions:

Version 5.2 << LinearAlgebra`MatrixManipulation`; LowerDiagonalMatrix[a, 5] // MatrixForm
Version 5.2 << LinearAlgebra`MatrixManipulation`; UpperDiagonalMatrix[a, 5] // MatrixForm
Version 5.2 << LinearAlgebra`MatrixManipulation`; TridiagonalMatrix[a, 5] // MatrixForm

LUMatrices can be replaced by the following definition:

Version 5.2 << LinearAlgebra`MatrixManipulation`; LUMatrices[First@LUDecomposition[{{1., 2.}, {3., 4.}}]]

SquareMatrixQ can be replaced by the following definition:

Version 5.2 << LinearAlgebra`MatrixManipulation`; SquareMatrixQ[{{x}}]

Construct a zero matrix:

Version 5.2 << LinearAlgebra`MatrixManipulation`; ZeroMatrix[2] // MatrixForm

Compute the polar decomposition of a matrix:

Version 5.2 << LinearAlgebra`MatrixManipulation`; PolarDecomposition[{{1, 1}, {1, I}}] // RootReduce

Display the structure of a matrix:

Version 5.2 << LinearAlgebra`MatrixManipulation`; MatrixPlot[Reverse@IdentityMatrix[10]]

These functions were available in previous versions of Mathematica and are now available on the web at library.wolfram.com/infocenter/MathSource/6770:

LinearEquationsToMatrices
InverseMatrixNorm
MatrixConditionNumber