vecd

The <code>vecd</code> operator as used by schwartzman2008in;textualTFORGE flattens a symmetric matrix into a vector of unique elements such that the Frobenius norm of the matrix equals the Euclidean norm of the vector. This means that the off-diagonal elements are scaled by \(\sqrt{2}\).
In the returned vector the diagonal elements are first then the (scaled) off-diagonal elements; this ordering is different to <code>vech()</code>.

The eigenvalues of observed symmetric matrices are often of intense scientific interest. This package offers single sample tests for the eigenvalues of the population mean or the eigenvalue-multiplicity of the population mean. For k-samples, this package offers tests for equal eigenvalues between samples. Included is support for matrices with constraints common to geophysical tensors (constant trace, sum of squared eigenvalues, or both) and eigenvectors are usually considered nuisance parameters. Pivotal bootstrap methods enable these tests to have good performance for small samples (n=15 for 3x3 matrices). These methods were developed and studied by Hingee, Scealy and Wood (2026, "Nonparametric bootstrap inference for the eigenvalues of geophysical tensors", accepted by the Journal of American Statistical Association). Also available is a 2-sample test using a Gaussian orthogonal ensemble approximation and an eigenvalue-multiplicity test that assumes orthogonally-invariant covariance.

Kassel Liam Hingee

TFORGE

Tests for Geophysical Eigenvalues

Art B. Owen

Board of Trustees Leland Stanford Junior University

vecd function

<dl><dt>m</dt>
<dd>A symmetric matrix</dd></dl>

Arguments

Flatten a symmetric matrix into a vector preserving Frobenius norm. — vecd

<dl>

<dt>m</dt>
<dd>A symmetric matrix</dd>

</dl>

vecd: Flatten a symmetric matrix into a vector preserving Frobenius norm.

Description

Usage

Value

Arguments

Details

References

Examples