Abstract: An optical system affixed to an electronic apparatus is provided, including a first optical module, a second optical module, and a third optical module. The first optical module is configured to adjust the moving direction of a first light from a first moving direction to a second moving direction, wherein the first moving direction is not parallel to the second moving direction. The second optical module is configured to receive the first light moving in the second moving direction. The first light reaches the third optical module via the first optical module and the second optical module in sequence. The third optical module includes a first photoelectric converter configured to transform the first light into a first image signal.

Abstract: The present disclosure provides a matrix device and an operation method thereof. The matrix device includes a transpose circuit and a memory. The transpose circuit is configured to receive a first element string representing a native matrix from a matrix source, wherein all elements in the native matrix are arranged in the first element string in one of a “row-major manner” and a “column-major manner”. The transpose circuit transposes the first element string into a second element string, wherein the second element string is equivalent to an element string in which all elements of the native matrix are arranged in another one of the “row-major manner” and the “column-major manner”. The memory is coupled to the transpose circuit to receive the second element string.

Abstract: An optical system affixed to an electronic apparatus is provided, including a first optical module, a second optical module, and a third optical module. The first optical module is configured to adjust the moving direction of a first light from a first moving direction to a second moving direction, wherein the first moving direction is not parallel to the second moving direction. The second optical module is configured to receive the first light moving in the second moving direction. The first light reaches the third optical module via the first optical module and the second optical module in sequence. The third optical module includes a first photoelectric converter configured to transform the first light into a first image signal.

Abstract: The present invention relates to a system and method for an electronic identification system to identify formats of electronic certificate and identification. At least one ticket holder can buy an electronic certificate through a web site certified by the electronic identification system and use the electronic certificate to check-in or for identity confirmation. The electronic identification system can also analyze statistical data, verify the electronic certificate, and notify at least one ticket supplier about current attendance and the consumer information immediately.