The generalized inverses of tensors via the C-Product

This paper studies the issues about the generalized inverses of tensors under the C-Product. The aim of this paper is threefold. Firstly, this paper present the definition of the Moore-Penrose inverse, Drazin inverse of tensors under the C-Product. Moreover, the inverse along a tensor is also introduced. Secondly, this paper gives some other expressions of the generalized inverses of tensors by using several decomposition forms of tensors. Finally, the algorithms for the Moore-Penrose inverse, Drazin inverse of tensors and the inverse along a tensor are established

VISUAL AUDIO MESSAGES

Computing devices (e.g., a cellular phone, a smartphone, a desktop computer, a laptop computer, a tablet computer, a portable gaming device, a watch, etc.). may enable users to exchange electronic communication including both a recorded message, such as an audio recording, a video recording, etc., as well as a transcript of the recorded message. In some examples, a first computing device may record audio from a first user and perform speech-to-text to generate a transcript of the recorded audio. The first computing device may then send the recorded message and the transcript of the recorded message in a single electronic communication to a second computing device (e.g., being used by a second user). Because the electronic communication includes the recorded message and the transcript of the recorded message, the second user can both listen to and read the recorded message, which may improve consumption of the recorded message (e.g., because background noise may make listening to the recorded message difficult, reading a transcript of the recorded message may be faster than listening to the recorded message, etc.). To facilitate a hands-free user experience, the computing device may include a voice user interface (VUI) by which a user may compose the electronic communication. For example, the user may provide voice commands (e.g., “clear”, “send”, “browse”, etc.) to cause the computing device to perform corresponding functions with respect to the electronic communication. Furthermore, the computing device may provide one or more instructions for using voice commands. In some cases, the instructions may relate to the action currently being taken by the user, a context of the electronic communication, etc