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I would like to remove the leading space that appears on the left before the equation on the latex below.

&{\bf y}_{l} = \sum _{k=1}^{L} {\bf H}_{l,k} {\bf x}_{k}+ {\bf w}_{l} &{{(1)}}
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I cant post a comment yet so I am giving an answer instead.

If you want to left align the equation, you can use

&{\bf y}_{l} = \sum _{k=1}^{L} {\bf H}_{l,k} {\bf x}_{k}+ {\bf w}_{l} &{{(1)}}

if that's what you mean by "remove the leading space".

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