= Stata Matrices =

'''Matrices''' are a data type used for meta programming in the Stata programming language. See also [[Stata/Scalars|scalars]].

<<TableOfContents>>

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== 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.

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== 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 [[Stata/Scalars|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)`        ||

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== See also ==

[[https://www.stata.com/manuals/u14.pdf|Stata manual section 14: Matrix expressions]]



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