You got your new Samsung Galaxy Note 10.1. If you like to use S Pen or you need to draw etc, Galaxy Note is good tablet to have. Apple has AirPlay for its devices. Samsung has its own solution called AllShare Play to stream music, photos, videos to other dlna devices.
You can connect Galaxy Note & HDTV using a physical HDMI cable or MHL cable. But it won’t be mobile as you can’t move with the tablet. You need to use AllShare Play instead.
AllShare Play android app lets you play media stored on your samsung tablet to other dlna compatible devices like Samsung Internet TVs, Blu-ray/DVD Players, Google TV, Other Smart TVs etc. If you want to connect to TV via other devices like Apple TV, Xbox 360, PS3 etc, read 6 android apps for AirPlay.
How to use AllShare Play on Galaxy Note 10.1 for AirPlay
1. Make sure your Galaxy Note 10.1 & DLNA device both are connected same WiFi network.
2. Open the video or photo you want to display on the TV, It displays AllShare Play icon if it finds any DLNA devices.
You should be able to control the video or photos from your galaxy note 10.1. Google Play Store has popular android apps to stream media from your android devices to other devices.
Using AllShare Play, You can also access content of other AllShare Play compatible devices like Galaxy S3 etc on your Galaxy Notes 10.1. AllShare is available on Samsung Products like Galaxy S2, Galaxy S etc