Weinstein-Aronszajn identity
التعريفات والمعاني
== English ==
=== Etymology ===
(This etymology is missing or incomplete. Please add to it, or discuss it at the Etymology scriptorium.)
=== Proper noun ===
the Weinstein-Aronszajn identity
(mathematics) An identity stating that if
A
{\displaystyle A}
and
B
{\displaystyle B}
are matrices of size m × n and n × m respectively (either or both of which may be infinite) then, provided
A
B
{\displaystyle AB}
(and hence, also
B
A
{\displaystyle BA}
) is of trace class,
det
(
I
m
+
A
B
)
=
det
(
I
n
+
B
A
)
,
{\displaystyle \det(I_{m}+AB)=\det(I_{n}+BA),}
where
I
k
{\displaystyle I_{k}}
is the k × k identity matrix.