Let $M\in R^{M\times N}$, a function $f: M\rightarrow R$ is called convex on $M$ if
$f\big((1-\lambda)X1+\lambda X2, (1-\lambda)Y1+\lambda Y2\big) \leq (1-\lambda)f(X1,Y1) + \lambda f(X2,Y2)$
For all $(X1,Y1)\in M$ and $(X2,Y2)\in M$ and all $\lambda\in[0,1]$.
Is the above definition correct for multivariate function?