NB: I stopped using Matrix because the organisation is shitty and the mod tools are non-existant.

• Element - The default web-based client. Used to be called 'Riot'
• Cinny - More Discord-like interface.
• Fractal - Gnome's chat client.
• Quaternion - Qt-based client.
• NeoChat
• Nheko
• Thunderbird is also working on support.

• Clients on the Matrix homepage.

There's no standard way to link to a Matrix user or room like there is with say E-mail or XMPP¹⁾.

But you can use matrix.to to generate a Hyperlink.

• matrix.org
• Matrix_(protocol)