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How to handle out of domain utterances in Amazon Alexa

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up vote 0 down vote favorite I had different intents in the skill, I am using php as service. Everything is working fine, but if the user ask utterances that are not configured in any of the intents, it must go to the else part. Eg code is as follows:- if($EchoReqObj->request->type=="LaunchRequest"){ $text = "Testing launch"; $array = array("version"=>"1.0","response"=>array("outputSpeech"=>array("type"=>"PlainText","text"=>$text),"shouldEndSession"=>false)); echo json_encode($array); } else if(getting the intent name){//Do something.} else{ $text = "In else part"; $array = array("version"=>"1.0","response"=>array("outputSpeech"=...

prove Gram's determinant invariant under orthogonalisation

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up vote 0 down vote favorite let $mathcal H$ be a Hilbert space, and let $g_1,...g_nin mathcal H$ . let $G(g_1,...g_n)$ be Gram's determinant: $left|{begin{array}{ccc} left(g_{1},g_{1}right) & dots & left(g_{1},g_{n}right)\ vdots & ddots & vdots\ left(g_{n},g_{1}right) & dots & left(g_{n},g_{n}right) end{array}}right|$ write $(h_1,...h_n)$ to be the result of orthogonalisating $(g_1,...g_n)$ , without normalizing the vectors . I want to show that $G(g_1,...g_n)=G(h_1,...h_n)$ It's not hard to see that suffices to show $G(g_1,...g_n)=G(g_1,h_2,g_3,...g_n)$ when $h_2=g_2+alpha g_1$ , such that $g_1perp h_2$ . but I didn't manage to finish that up. I tried to calculate it directly, but it gets mass. functional-analysis hilbert-spaces ...