Yes.

I don't know whether yours can or not.  However, my desktop (wired ethernet)
and my laptop (wireless) work quite well together.
Jim

one way is if your linksys router is a so-called Wireless Router
They support wired and wireless  (yes, simultaneously)

if it is just a wired router, then you need to connect a "wireless
access point".
That effectively makes it like a so-called Wireless Router.

I don't use wireless.. But I'm a bit of a geek.. Truth is most people
don't know what a Router is. What a switch is..   I knew those basics
from a book called networking first step..  That was all theory. Not
practical at all. But maybe don't bother with that, since you probably
haven't even built your own computer, so you're not that much of a
geek.

It took me a while to figure out how it relates to the things being
sold.. I guess I read one or two usenet posts that made little things
click.. Maybe chatted to a few people on IRC chat..  But unlike that
book I mentioned.  The so-called Routers being sold today, are best
termed NAT Routers, and their sockets are not Router sockets, but
Switch sockets (maybe L3 switch).

Understand that with Wired, what they call a Router, means typically
get a NAT Router with a switch built in.
That's your linksys machine with many sockets.  Sometimes they have a
modem built in there too. So it's more than just a NAT Router with a
switch.. And it has a DHCP server in there handing out IPs.  So it's
alot.  It's your typical NAT Router.

Wireless Routers, Are   Wired Routers, but they have a wireless switch
built in. A wireless switch is called an "access point".
They also have a wired switch built in, that's the way they get the
many sockets to plug computers into.

So you can built a wireless router by using a wired router and a
wireless access point.

And you need your computers to have a wireless adaptor..  Either built
in or external like PCMCIA or USB.  The former should have an antenna.
If going USB, most are sold without antennae, but the one with them
have better range I have heard.

I guess you're not that much of a geek, or you would have built your
own..!