2 Changed "inner product" to "bilinear forms" after a comment suggested this.

# Notation for "innerproduct"bilinearform $y^t M z$, where $M$ is a matrix and $y,z$ are vectors.

I'm working on a problem where I need to consider "inner products" a bilinear form of the form $y^t M z$ where $M$ is an $n$-by-$n$ real symmetric matrix and $y,z \in \mathbb{R}^n$ are vectors. I also need to consider restricted forms of such a product, of the form $$\sum_{i,j=1}^n y_i m_{ij} z_j \mathbf{I}_{(y_i,z_j) \in E},$$ where $E$ is some subset of $\mathbb{R}^2$. We recover $y^t M z$ by taking $E=\mathbb{R}^2$. I want a common notation for $y^t M z$ and for these restricted sums, so I have been writing $y^t M z = \langle y,z\rangle_M$, and writing $\langle y,z\rangle_{M,E}$ for the restricted sum above.

I see nothing wrong with the notation I'm using. However, if there's a standard notation for such things that I am unaware of, I would like to know about it. Is there? If you know of another notation, can you give me a reference?

1

# Notation for "inner product" $y^t M z$, where $M$ is a matrix and $y,z$ are vectors.

I'm working on a problem where I need to consider "inner products" of the form $y^t M z$ where $M$ is an $n$-by-$n$ real matrix and $y,z \in \mathbb{R}^n$ are vectors. I also need to consider restricted forms of such a product, of the form $$\sum_{i,j=1}^n y_i m_{ij} z_j \mathbf{I}_{(y_i,z_j) \in E},$$ where $E$ is some subset of $\mathbb{R}^2$. We recover $y^t M z$ by taking $E=\mathbb{R}^2$. I want a common notation for $y^t M z$ and for these restricted sums, so I have been writing $y^t M z = \langle y,z\rangle_M$, and writing $\langle y,z\rangle_{M,E}$ for the restricted sum above.

I see nothing wrong with the notation I'm using. However, if there's a standard notation for such things that I am unaware of, I would like to know about it. Is there? If you know of another notation, can you give me a reference?