You are currently browsing the tag archive for the ‘transpose
operator’ tag. When studying a mathematical space X (e.g. a
vector space, a topological space, a manifold, a group, an
algebraic variety etc.), there are two fundamentally basic ways
to try to understand the space: - By looking at subobjects in X,
or more generally maps from some other space Y into X. For
instance, a point in a space X can be viewed as a map from to X;
a curve in a space X could be thought of as a map from to X; a
group G can be studied via its subgroups K, and so forth. - By
looking at objects on X, or more precisely maps from X into some
other space Y. For instance, one can study a topological space X
via the real- or complex-valued continuous functions on X; one
can study a group G via its quotient groups ; one can study an
algebraic variety V by studying the polynomials on V (and in
particular, the ideal of polynomials that vanish identically on
V); and so forth. (There are also more sophisticated ways to
study an object via it