If you want to hide, for example, the_author_meta('linkedin');
if no data exists for that field, then you could just do the following
<?php if(!empty(get_the_author_meta('linkedin'))) { ?>
<a href="https://wordpress.stackexchange.com/questions/187400/<?php the_author_meta("linkedin'); ?>" target="_blank"><i class="fa fa-linkedin-square" title="LinkedIn"></i></a>
<?php } ?>`
and then apply similar logic to other fields. If this is not what you were asking, then you should explain a little more about what you are trying to accomplish.