The Operator Trigonometry in Statistics

Operator trigonometry of multivariate finance

“…These entities play important roles in the applications of the operator trigonometry to statistics [4][5][6][7], and we would also expect them to do so in multivariate finance. Possibly in a successor paper we or others will pursue the details for sufficiently interesting financial instrument applications.…”

“…We will assume that the interested reader will go to the references [1][2][3][4][5][6][7] for more information. The easiest and most complete theory is for A an n × n symmetric positive definite (SPD) matrix with eigenvalues 0 < λ n λ n−1 · · · λ 1 .…”

The Trigonometry of Matrix Statistics

“…Because it may be assumed that the readers of this journal will know most or all of the statistical methods and theories which will be discussed in this review, I will place more emphasis in this paper on first explaining this author's matrix trigonometry in basic terms, and then explaining how it may be connected to matrix statistics. This author Gustafson ( , 2001Gustafson ( , 2002 was the first to make those connections.…”

“…And until my paper , see also Gustafson (2001Gustafson ( , 2002, no one explicitly connected my matrix trigonometry to statistics.…”

“…In this and succeeding sections I will summarize some applications of the matrix trigonometry to statistics to date. These began in Gustafson ( , 2002Gustafson ( , see also 2001. The reader is referred in particular to Gustafson (2002) for more details.…”