# Commit 2023-03-17 14:58 9f0d61b4

View on Github →fix(analysis/inner_product_space/pi_L2): add missing type cast functions (#18574)
The preferred way to convert between `ι → 𝕜`

and `euclidean_space 𝕜 ι`

is via `pi_Lp.equiv`

, as this preserves the right typing information.
We use the local notation `⟪x, y⟫ₑ`

to refer the euclidean inner product of `x y : ι → 𝕜`

, which inserts the casting within the notation.
This adds a new definition `matrix.to_euclidean_lin`

as a shorthand to turn a matrix into a `linear_map`

over `euclidean_space`

.
It also generalizes `inner_matrix_row_row`

and `inner_matrix_col_col`

away from `fin n`

to arbitrary index types.