Update flag inside array of objects

I've this document:

{
    "_id" : ObjectId("540d881d475d68010693e340"),
    "notes" : [ 
        {
            "owner" : null,
            "creation" : 1411641315424,
            "text" : "test rec",
            "action" : "0",
            "recipients" : [ 
                {
                    "username" : "root",
                    "read" : false
                }, 
                {
                    "username" : "zivolof",
                    "read" : false
                }
            ]
        },
        {
            "owner" : null,
            "creation" : 1411641315424,
            "text" : "test rec",
            "action" : "0",
            "recipients" : [ 
                {
                    "username" : "root",
                    "read" : false
                }, 
                {
                    "username" : "zivolof",
                    "read" : false
                }
            ]
        }
    ]
}

I find it with this query:

{
    "_id": id, 
    "notes.recipients": {
         $elemMatch: {
            username: username, 
            read: false
        }
    }
}

I then need to update the read flag of the entire document to true. How can I do?