This means that " A " is unitarily equivalent ( i . e . similar, using a unitary matrix as change of basis ) to an upper triangular matrix; this follows by taking an Hermitian basis for the flag.
42.
Movement in a linear fashion is achieved, principally, by a " step and slide . " The fighter will first move to the desired'point'on the triangular matrix, then swiftly slide one's rear leg to meet his leading foot.
43.
By the LU decomposition algorithm, an invertible matrix may be written as the product of a lower triangular matrix " L " and an upper triangular matrix " U " if and only if all its leading principal minors are non-zero.
44.
By the LU decomposition algorithm, an invertible matrix may be written as the product of a lower triangular matrix " L " and an upper triangular matrix " U " if and only if all its leading principal minors are non-zero.
45.
From this it is easily seen that all three matrices have determinant 1, as the determinant of a triangular matrix is simply the product of its diagonal elements, which are all 1 for both " L n " and " U " " n ".
46.
:* \ Theta _ i = \ Phi _ i P, where P is a lower triangular matrix obtained by a Cholesky decomposition of \ Sigma _ u such that \ Sigma _ u = PP', where \ Sigma _ u is the covariance matrix of the errors u _ t
47.
The variable " L " ( standing for lower or left ) is commonly used to represent a lower triangular matrix, while the variable " U " ( standing for upper ) or " R " ( standing for right ) is commonly used for upper triangular matrix.
48.
The variable " L " ( standing for lower or left ) is commonly used to represent a lower triangular matrix, while the variable " U " ( standing for upper ) or " R " ( standing for right ) is commonly used for upper triangular matrix.
49.
The second equation follows from the fact that the determinant of a triangular matrix is simply the product of its diagonal entries, and that the determinant of a permutation matrix is equal to ( " 1 ) " S " where " S " is the number of row exchanges in the decomposition.
50.
Once the divergences between all pairs of samples have been determined, the resulting triangular matrix of differences is submitted to some form of statistical cluster analysis, and the resulting dendrogram is examined in order to see whether the samples cluster in the way that would be expected from current ideas about the taxonomy of the group, or not.
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