G.7 PROPERTIES OF TRACE AND DETERMINANT
Definition: Trace The trace of square matrix is
(G.53)
where {ann} are the diagonal elements of A.
The trace has the following properties:
- Eigenvalues :
(G.54)
- Addition and multiplication by scalars {c, d}:
(G.55)
- Associative pairwise: tr[AB] = tr[BA] and
(G.56)
(G.57)
- Kronecker product:
(G.58)
- Similarity invariant:
(G.59)
for invertible matrix P. - Bounds for PSD matrices A and B:
(G.60)
The determinant of square matrix has the following ...
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