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Explore Stack Internal$\langle{u_i,m_j}\rangle$ is just an inner product on a vector space $\mathcal{V}$, i.e. a function $\langle{u_i,m_j}\rangle: \mathcal{V} \times \mathcal{V} \to \mathbb{R}, $ which follows 3 axioms (linearity in $u_i$,symmetric,positive definite). Therefore it $r_{i,j}$ is just a scalar value. This is essentially the dot product as @Kristina says but in a more generalised form for vector spaces.
$\langle{u_i,m_j}\rangle$ is just an inner product on a vector space $\mathcal{V}$, i.e. a function $\langle{u_i,m_j}\rangle: \mathcal{V} \times \mathcal{V} \to \mathbb{R}, $ which follows 3 axioms (linearity in $u_i$,symmetric,positive definite). Therefore it $r_{i,j}$ is just a scalar value. This is essentially the dot product as @Kristina says but in a more generalised form for vector spaces.
$\langle{u_i,m_j}\rangle$ is just an inner product on a vector space $\mathcal{V}$, i.e. a function $\langle{u_i,m_j}\rangle: \mathcal{V} \times \mathcal{V} \to \mathbb{R}, $ which follows 3 axioms (linearity in $u_i$,symmetric,positive definite). Therefore $r_{i,j}$ is just a scalar value. This is essentially the dot product as @Kristina says but in a more generalised form for vector spaces.
$\langle{u_i,m_j}\rangle$ is just an inner product on a vector space $\mathcal{V}$, i.e. a function $\langle{u_i,m_j}\rangle: \mathcal{V} \times \mathcal{V} \to \mathbb{R}, $ which follows 3 axioms (linearity in $u_i$,symmetric,positive definite). Therefore it $r_{i,j}$ is just a scalar value. This is essentially the dot product as @Kristina says but in a more generalised form for vector spaces.
