Type Definitions
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Root
Data type holding roots of a polynomial with multiplicity.
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Description
Roots are counted with multiplicity:
[x, m]indicates a root of a polynomial at the (Complex or real) numberxwith multiplicitym. A Root can also be a simple number or Complex number, which is taken to have multiplicity equal to 1.Details
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Pivot
A pivot position is recorded as a pair
[row, column]. -
Details
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PLUData
The core data computed by Gaussian elimination.
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Description
When performing Gaussian elimination on a computer, it is easy to keep track of the row operations performed, and various other data.
Properties
Name Type Description PArray.<number> A permutation of the numbers
1...m-1. by Matrix.permutation.LMatrix An
mxmlower-triangular matrix with ones on the diagonal.UMatrix An
mxnmatrix in row echelon form.EMatrix An
mxminvertible matrix equal toL^(-1)P, soEA = U.pivotsArray.<Pivot> An array of pivot positions.
detnumber The determinant of the matrix (only set for square matrices).
Details
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QRData
The data computed in the Gram–Schmidt algorithm.
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Description
This primarily consists of an
mxnmatrixQwith orthogonal columns and an upper-triangularnxnmatrixRsuch thatA = QR. Also included is a list of which columns ofQare zero.Properties
Name Type Description QMatrix An
mxnmatrix with orthogonal columns.RMatrix An
nxnupper-triangular matrix.LDArray.<number> A list of the zero columns of
Q.Details
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Diagonalization
Diagonalizability data:
this = CDC^(-1). -
SVDData
Singular value decomposition data.
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LDLTData
LDLT decomposition data.