- #1

Peter_Newman

- 85

- 6

Hello,

I would like to reproduce the following equation, but I don't quite understand how to do the transformation:

$$ \sum_{i=1}^k \left( \frac{\langle y , x_i^* \rangle}{\sqrt{\langle x_i^*, x_i^* \rangle}} \right)^2 = \langle y, y \rangle$$

Where ##x_1^*,...,x_k^*##, are orthogonalized Gram-Schmidt vectors of ##x_1,...,x_k \in \Lambda## and ##y \in span(x_1^*,...,x_k^*) = span(x_1,...,x_k)##.

I would be very grateful for any helpful hints!

I would like to reproduce the following equation, but I don't quite understand how to do the transformation:

$$ \sum_{i=1}^k \left( \frac{\langle y , x_i^* \rangle}{\sqrt{\langle x_i^*, x_i^* \rangle}} \right)^2 = \langle y, y \rangle$$

Where ##x_1^*,...,x_k^*##, are orthogonalized Gram-Schmidt vectors of ##x_1,...,x_k \in \Lambda## and ##y \in span(x_1^*,...,x_k^*) = span(x_1,...,x_k)##.

I would be very grateful for any helpful hints!

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