Block Diagonal Matrix

A block diagonal matrix, also called a diagonal block matrix, is a block matrix whose diagonal blocks are square matrices and whose off-diagonal blocks are zero matrices. The diagonal blocks may have different sizes, including . Thus, a block diagonal matrix generalizes a diagonal matrix.

Block diagonal matrices are constructed in the Wolfram Language using BlockDiagonalMatrix[blocks], where blocks is a list of square matrices. Applying Normal gives an ordinary matrix. For example,

Normal[BlockDiagonalMatrix[{{{1}}, {{2, 3}, {4, 5}}}]]

returns the matrix