Using a 302 instead of a 301

[NextGenEDU]

I am trying to figure out the best way to garner the most amount of link value.

We have an app that lives on a sub-domain ... For the purposes of this question, let's call it app.mydomain.com.  We provide a service with this app that requires clients (with very high ranking websites) to link into app located on the sub-domain.

Would I garner more authority if had the high ranking client website link into a url that wasn't a sub-domain and redirect it using a 302?

For example:  What if I created a 302 that was www.mydomain.com/app and have it redirected to the sub-domain version of app.mydomain.com?

Additionally am I correct to assume that a 301 would merely pass that value to the sub domain and NOT provide much value to the root?

[Copstead]

What subdomain are you trying to get link juice for?  app.mydomain.com or www.mydomain.com?

Never use a 302.  You lose 100% of link juice.

With a 301, you will still lose a little, maybe 10% or so, but you will pass the link juice on to the app.mydomain.com

But if you are trying to get the most Link Juice to the root domain mydomain.com, then I would just suggest linking directly to the app.mydomain.com

[SEOExecutive20]

It seems your on the righ track as a 302 Redirect is a temporary redirect
and passes 0% of link juice according to SEOMOZ: http://www.seomoz.org/learn-seo/redirection

Also The "root domain" redirected page will still retain its PageRank, MozRank,
Page Authority and Traffic Value – and the detour page will not accumulate any.

You are also correct about the 301:
A 301 Redirect is a permanent redirect which passes between 90-99% of link juice
according to SEOMOZ: http://www.seomoz.org/learn-seo/redirection

Keep in mind that on this same page SEOMOZ goes on to say "and in most cases (302 redirect) should not be used.
Also if kept to long a 302 will eventually slide in rankings

I think yes you will garner more link value using a subfolder then a subdomain
As you will see posted also on SEOMOZ:

"5. Subdomains or Sub-folders
Since search engines keep different metrics for domains than they do subdomains,
it is recommended that webmasters place link worthy content like blogs in subfolders
rather than subdomains. (i.e. www.example.com/blog/ rather than blog.example.com)
The notable exception to this is language specific websites. (i.e. en.example.com for english)"

http://www.seomoz.org/learn-seo/domain

But the main point here is will you gain anything to your root domain while it
has a 302 and redrecting to another page

Personally, I would avoid the 302 and move the page "app.mydomain.com" to the subfolder "www.mydomain.com/app"
Having the old page url "app.mydomain.com" 301 redirect to the subfolder "www.mydomain.com/app"
passing 90-99% of the juice

[NextGenEDU]

Just to clarify, I want to direct the link juice to: www.mydomain.com from app.mydomain.com.  As these high profile websites will be linking to the app.

My idea was to have them link to a page on the www.mydomain.com/app that I would effectively redirect back to app.mydomain.com.

But if I use a 301, the 301 will direct link juice back toward the sub domain (app.mydomain.com).

So my question is ... will the 302 keep the juice at the www version (not pass the juice)

Hopefully this makes sense.  The other option is to simply let them link to the app. and add a canonical tag that points the juice back to the www version.