matrices

An overview

In Macaulay 2, each matrix is defined over a ring, (see rings). Matrices are perhaps the most common data type in Macaulay 2.

For an overview of matrices as homomorphisms between modules, see homomorphisms of modules. For additional common operations and a comprehensive list of all routines in Macaulay 2 which return or use matrices, see Matrix.

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making matrices

• inputting a matrix
• projections, inclusions, and permutations
• random and generic matrices

operations involving matrices

• extracting information about a matrix
• basic arithmetic of matrices
• concatenating matrices
• submatrices
• differentiation

determinants and related computations

• rank of a matrix
• determinants and minors
• Pfaffians
• exterior power of a matrix

display of matrices and saving matrices to a file

• format and display of matrices in Macaulay 2
• importing and exporting matrices