On the Linear Algebraic Monoids Associated to Congruence of Matrices

Himadri Mukherjee, Gunja Sachdeva

This paper discusses the generalized congruence equation $X^{t}AX=B$, for $X\in M_n(k)$ over any field $k$, through the action of monoid $Sol_A \times Sol_B := \{X \ | \ X^tAX = A\}…