Matrix Calculations

Calculation

Provides a space to enter an expression for the calculation. This can be typed in directly or built up by clicking names in the Available Data or Standard Matrices lists together with operators or functions.

Available Data

This lists the matrices (rectangular, symmetric and diagonal) and their sizes (rows x columns) that are available for calculations. Rectangular, symmetric and diagonal matrices names are prefixed with M:, S: and D: respectively to display the type of each matrix. This list can be supplemented with variates and scalars using the Available Data Includes option. Double-clicking an identifier name will copy the name into the calculation field at the current cursor position.

Available Data Includes

These options allow scalars and variates to be displayed in the Available Data list.

Scalars (N:)		scalars will be displayed in the Available Data list with the name prefixed with a N:.
Variates (V:)		variates will be displayed in the Available Data list with the name prefixed with a V:.

Save In

Specifies the name of the matrix (or scalar) to save the result from the calculation.

Display in Spreadsheet

When selected, the matrix resulting from the calculation will be displayed in a spreadsheet.

Print in Output

When selected, the matrix resulting from the calculation will be printed in the Output window.

Standard Matrices

This lists various standard matrices that are available for calculations. The size of the standard matrix is specified in the rows and Columns fields. Double-clicking a matrix type in the list will copy the name within the calculation field at the current cursor position.

Operations

These buttons specify various matrix operations. Clicking a button will place that function into the calculation list. If text is currently selected in the calculation field, then this will be inserted as the first argument of the function.

Operation	GenStat expression	Definition	Description
Product	A *+ B	AB	matrix product or multiplication
Trace	TRACE(A)	tr A	the trace of a matrix.
Direct Product	DPRODUCT(A;B)	A Ä B	matrix direct product.
Transpose	T(A)	A'	matrix transpose
Diagonal	DIAGONAL(A)		extract the diagonal of a matrix.
Quadratic Product	T(A)+X+A	A'XA	matrix quadratic product.
Inverse	INVERSE(A)	A^-1	the inverse of a matrix.
Determinant	DET(A)	\|A\|	the determinant of a matrix.
Choleski Decomp.	CHOLESKI(A)	L: A = LL'	- the Choleski decomposition of a matrix.
Eigenvalues	EVALUES(A)		the eigenvalues of a matrix.
Eigenvectors	EVECTORS(A)		the eigenvectors of a matrix.
Singular Values	SVALUES(A)		the singular values of a matrix.
Left Singular Vectors	LSVECTORS(A)		the left singular vectors of a matrix.
Right Singular Vectors	RSVECTORS(A)		the right singular vectors of a matrix.

Elementwise

These buttons specify various scalar operations that will be applied to each element of the matrix. Clicking the button will place the function into the calculation list. If text is currently selected in the calculation field, then this will be inserted as the first argument of the function.

Operation Description

+ elementwise addition.

- elementwise subtraction.

* elementwise multiplication.

/ elementwise division.

Exp elementwise exponential function.

Log e elementwise natural logarithm.

Sqrt elementwise square root.

Abs elementwise absolute value.

Note that the dimensions of the two matrices must match exactly for the operators +, -, * and /.

Additional Functions

This opens a functions dialog where you can select a function from a more general set of functions.

Action Buttons

Run	Run the calculation.
Cancel	Close the menu without further changes.

Operation	Description
+	elementwise addition.
-	elementwise subtraction.
*	elementwise multiplication.
/	elementwise division.
Exp	elementwise exponential function.
Log e	elementwise natural logarithm.
Sqrt	elementwise square root.
Abs	elementwise absolute value.