# Questions tagged [inner-products]

For questions about inner products and inner product spaces, including questions about the dot product.

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### Show that the inner product of two square summable series converges [closed]

Given that x and y are convergent square summable series, show that the inner product converges as well, i.e. the sum to infinity of xy
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### Consequences of definition of scalar product

Definition: Let $V$ be a vector space over the field $K=\mathbb{R}$ (or over $K=\mathbb{C})$. The scalar product on $V$ is a function $V\times V\to K,$ denoted by $(x,y)\mapsto \langle x,y\rangle$, ...
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### The positive/negative sign in inner product involve diagonal matrix and basis transformation matrix.

The expression of one inner product is $<\pi PDEP^{-1}, \pi PD^2EP^{-1}>$. Here, $\pi$ is a row vector that has strictly non-negative terms, D is a diagonal matrix with non-positive diagonal ...
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### Effect of Basis Change on Absolute Vector Magnitudes

Does Basis Change Affect the Absolute Magnitude of Vectors? How does a change in basis impact the absolute length of vectors? I'm trying to understand the effect of a basis change on the absolute ...
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### Is a scalar presented as a matrix or not here?

In the linear algebra course I am taking, the inner product of 2 vectors $\langle u, v \rangle$ is defined as being a scalar; however, it is also viewed as being a product of 2 matrices as $u^Tv$, as ...
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