# Grassmannian frames in the Grassmannian

I am new to the Grassmannian. I have read about Grassmannian frames in $\mathbb R^n$. My question is can we define Grassmannian frames in a Grassmannian space $Gr(k,n)$ just like in $\mathbb R^n$? That is if we define a frame $X=(x_1,\dots,x_N)$ where $x_i\in Gr(k,n)$ what is the innerproduct $\langle x_1,x_2\rangle$?

• Take a look at the paper by Joel Rouyer entitled "On $p$-tuples of the Grassmann manifolds"; it looks relevant. Feb 7, 2014 at 23:23