Stata Matrices

Matrices are a data type used for meta programming in the Stata programming language. See also scalars.

Contents

Stata Matrices

Definition

To define a matrix, use either the matrix or matrix input command. The latter only allows literals in the definition, while the former allows expressions like 1/3 or _pi. The former also allows assignment by matrix arithmetic.

The matrix's values are bounded by parentheses (( and )). Values in a row are delimited with a comma (,). Rows are delimited with a backslash (\).

. matrix input A = (1,2\3,4)
. matrix list A
A[2,2]
   c1  c2
r1  1   2
r2  3   4

Matrices can be defined with other matrices as well.

. matrix B = (A,A)
. matrix list B
B[2,4]
   c1  c2  c1  c2
r1  1   2   1   2
r2  3   4   3   4

. matrix C = (A\A)
. matrix list C
C[4,2]
   c1  c2
r1  1   2
r2  3   4
r1  1   2
r2  3   4

A vector is simply a special case of a matrix.

Rows and Columns

A newly-defined matrix's rows and columns have sequential names (r1, r2, and so on).

Many commands return matrices with names rows and columns. Many more commands are able to parse passed matrices only because rows and columns are named in a structured way.

Usage

Matrixes can be joined in either direction.

. matrix A = (1)
. matrix B = A , (2)
. matrix list B
B[1,2]
   c1  c2
r1  1   2

. matrix C = B \ (3,4)
. matrix list C
C[2,2]
   c1  c2
r1  1   2
r2  3   4

A matrix is indexed by NAME[ROW,COL]. Indexing starts at 1. C[1,2] is 2 in the above example.

Arithmetic

Addition (and subtraction) is defined for any like-sized matrices.

Multiplication is defined for any a x b and b x c matrices, the result being a x c.

The transpose of matrix A is defined with A'.

The negation of matrix A is defined with -A.

Division by scalar is performed with the forward slash (/) operator.

The Kronecker product is performed with the hash (#) operator.

Functions

Matrices support these functions.

Function

cholesky(M)

corr(M)

diag(v)

get(systemname)

hadamard(M,N)

I(n)

inv(M)

invsym(M)

J(r,c,z)

matuniform(r,c)

nullmat(matname)

sweep(M,i)

vec(M)

vecdiag(M)

Matrices also support these functions which return a scalar.

Function

coleqnumb(M,s)

colnfreeparms(M)

colnumb(M,s)

colsof(M)

det(M)

diag0cnt(M)

el(M,i,j)

issymmetric(M)

matmissing(M)

mreldif(X,Y)

roweqnumb(M,s)

rownfreeparms(M)

rownumb(M,s)

rowsof(M)

trace(M)