Matrix Operations in Mata

Multivariate Analysis
Matrix Operations in Mata

Mata is the new interactive matrix command language that comes with Stata 9. To start Mata, type meta in the Stata command window. The end a Mata session, type end and press return.

The Matrix

: A = (2,1\3,2\-2,2)

: A

        1    2
    +-----------+
  1 |   2    1  |
  2 |   3    2  |
  3 |  -2    2  |
    +-----------+

Multiplication by a Scalar

: B = 3*A

: B

        1    2
    +-----------+
  1 |   6    3  |
  2 |   9    6  |
  3 |  -6    6  |
    +-----------+

Matrix Addition & Subtraction

: B = (1,1\4,2\-2,1)

: C = A + B

: C

        1    2
    +-----------+
  1 |   3    2  |
  2 |   7    4  |
  3 |  -4    3  |
    +-----------+
 
: D = A - B

: D
 
        1    2
    +-----------+
  1 |   1    0  |
  2 |  -1    0  |
  3 |   0    1  |
    +-----------+

Matrix Multiplication

: D = (2,1,3\-2,2,1)

: C = D*A

: C

        1    2
    +-----------+
  1 |   1   10  |
  2 |   0    4  |
    +-----------+

: C = A*D

: C

        1    2    3
    +----------------+
  1 |   2    4    7  |
  2 |   2    7   11  |
  3 |  -8    2   -4  |
    +----------------+

: D = (2,1,3)

: C = D*A

: C

        1    2
    +-----------+
  1 |   1   10  |
    +-----------+

: C = A*D
                       *:  3200  conformability error
                 :     -  function returned error

Transpose of a Matrix

: AT = A'

: AT

        1    2    3
    +----------------+
  1 |   2    3   -2  |
  2 |   1    2    2  |
    +----------------+

: ATT = AT'

: ATT

        1    2
    +-----------+
  1 |   2    1  |
  2 |   3    2  |
  3 |  -2    2  |
    +-----------+

Common Vectors

Unit Vector

: U = J(3,1,1)

: U

       1
    +-----+
  1 |  1  |
  2 |  1  |
  3 |  1  |
    +-----+

Common Matrices

Unit Matrix

: U = J(3,2,1)

: U

       1   2
    +---------+
  1 |  1   1  |
  2 |  1   1  |
  3 |  1   1  |
    +---------+

Diagonal Matrix

: S = (2,1,4\3,2,2\-2,2,3)

: S 

        1    2    3
    +----------------+
  1 |   2    1    4  |
  2 |   3    2    2  |
  3 |  -2    2    3  |
    +----------------+

: D = diag(S)

: D

[symmetric]
       1   2   3
    +-------------+
  1 |  2          |
  2 |  0   2      |
  3 |  0   0   3  |
    +-------------+

: V = (3,1,2)

: D = diag(V)

: D

[symmetric]
       1   2   3
    +-------------+
  1 |  3          |
  2 |  0   1      |
  3 |  0   0   2  |
    +-------------+
    
: E = diagonal(S)

: E
       1
    +-----+
  1 |  2  |
  2 |  2  |
  3 |  3  |
    +-----+

Identity Matrix

: I = I(3)

: I

[symmetric]
       1   2   3
    +-------------+
  1 |  1          |
  2 |  0   1      |
  3 |  0   0   1  |
    +-------------+

Symmetric Matrix

Using Stata

: C = (2,1,5\1,3,4\5,4,-2)

: C

[symmetric]
        1    2    3
    +----------------+
  1 |   2            |
  2 |   1    3       |
  3 |   5    4   -2  |
    +----------------+

: CT = C'

: CT

[symmetric]
        1    2    3
    +----------------+
  1 |   2            |
  2 |   1    3       |
  3 |   5    4   -2  |
    +----------------+

Inverse of a Square Nonsymmetric Matrix

: A = (4,2,2 \ 4,6,8 \ -2,2,4)

: A

        1    2    3
    +----------------+
  1 |   4    2    2  |
  2 |   4    6    8  |
  3 |  -2    2    4  |
    +----------------+

: AI = luinv(A)

: AI

          1      2      3
    +----------------------+
  1 |     1    -.5     .5  |
  2 |    -4    2.5     -3  |
  3 |   2.5   -1.5      2  |
    +----------------------+

Inverse & Determinant of a Square Symmetric Matrix

: C = (2,1,6\1,3,4\6,4,-2)

: CI = invsym(C)

: CI

[symmetric]
         1     2     3
    +-------------------+
  1 |   .6              |
  2 |  -.2    .4        |
  3 |    0     0     0  |
    +-------------------+

: d = det(C)

: d
-102

Number of Rows & Columns

: X = (3,2\2,-2\4,6\3,1)

: X

        1    2
    +-----------+
  1 |   3    2  |
  2 |   2   -2  |
  3 |   4    6  |
  4 |   3    1  |
    +-----------+

: r = rows(X)

: c = cols(X)

: r, c

       1   2
    +---------+
  1 |  4   2  |
    +---------+

: printf("rows = %f cols = %f", r, c)

rows = 4 cols = 2

Computing Column & Row Sums

: A = (2,1\3,2\-2,2)

: A

        1    2
    +-----------+
  1 |   2    1  |
  2 |   3    2  |
  3 |  -2    2  |
    +-----------+

: cs = colsum(A)

: cs

       1   2
    +---------+
  1 |  3   5  |
    +---------+

: rs = rowsum(A)

: rs

       1
    +-----+
  1 |  3  |
  2 |  5  |
  3 |  0  |
    +-----+

: s = sum(A)

: s

  8

Computing Column & Row Means

: cm = mean(A, 1) : cm 1 2 +-----------------------------+ 1 | 1 1.666666667 | +-----------------------------+ : rm = mean(A', 1) : rm 1 2 3 +-------------------+ 1 | 1.5 2.5 0 | +-------------------+

Horizontal Concatenation

: A = (2,1\3,2\-2,2) : A 1 2 +-----------+ 1 | 2 1 | 2 | 3 2 | 3 | -2 2 | +-----------+ : B = (1,1\3,4\2,2) : B 1 2 +---------+ 1 | 1 1 | 2 | 3 4 | 3 | 2 2 | +---------+ : C = A,B : C 1 2 3 4 +---------------------+ 1 | 2 1 1 1 | 2 | 3 2 3 4 | 3 | -2 2 2 2 | +---------------------+

Vertical Concatenation (Appending)

: = A\B : C 1 2 +-----------+ 1 | 2 1 | 2 | 3 2 | 3 | -2 2 | 4 | 1 1 | 5 | 3 4 | 6 | 2 2 | +-----------+

Matrix Subsetting

/* first create large matrix to be subset */ : A = (2,1\3,2\-2,2) : B = (1,1\3,4\5,0) : C = A,B\B,A : C 1 2 3 4 +---------------------+ 1 | 2 1 1 1 | 2 | 3 2 3 4 | 3 | -2 2 5 0 | 4 | 1 1 2 1 | 5 | 3 4 3 2 | 6 | 5 0 -2 2 | +---------------------+ /* create a matrix with 3kcolumns */ : D = C[1..., 1..3] : D 1 2 3 +----------------+ 1 | 2 1 1 | 2 | 3 2 3 | 3 | -2 2 5 | 4 | 1 1 2 | 5 | 3 4 3 | 6 | 5 0 -2 | +----------------+ /* create a matrix with 2 rows */ : D = C[1..2,1...] : D 1 2 3 4 +-----------------+ 1 | 2 1 1 1 | 2 | 3 2 3 4 | +-----------------+

Multivariate Course Page

Phil Ender, 22nov05, 4apr05

Multivariate Analysis Matrix Operations in Mata