We know matrices and their transposes and we also know flip matrices. In my previous paper <i>Matrices-One Review</i>, I introduced transprocal matrix. Flip matrices are transpose of transprocal matrices. ...We know matrices and their transposes and we also know flip matrices. In my previous paper <i>Matrices-One Review</i>, I introduced transprocal matrix. Flip matrices are transpose of transprocal matrices. Now I would like to introduce water image of four matrices said above and properties of such matrices. Also we know, determinant of sum of matrices is not equal to sum of determinant of matrices. Why can’t we get equal value on addition side and additive side of determinant of matrix addition and subtraction? This question triggered me to find the reason. The basic algebra of mensuration gave ideas to retreat determinant of matrix addition and subtraction. I extent that ideas for matrices sum. Further, in 1812, French mathematician <b>Jacques Philippe Marie Binet</b> described how to multiply matrices. Matrices are defined on addition, subtraction and multiplication but not in division. By the inspiration of Binet, I would like to describe how to do divisions on matrices. This idea is derived from division of fractions. In division of fraction, reciprocal of divisor fraction multiplies with dividend fraction. I do the same in division on matrices with some modifications. By this way, we could find quotient matrix and remainder matrix which satisfy division algorithm. So we could say, determinant of division of dividend matrix and divisor matrix is equal to division of determinant of dividend matrix and determinant of divisor matrix.展开更多
In order to apply compressive sensing in wireless sensor network, inside the nodes cluster classified by the spatial correlation, we propose that a cluster head adopts free space optical communication with space divis...In order to apply compressive sensing in wireless sensor network, inside the nodes cluster classified by the spatial correlation, we propose that a cluster head adopts free space optical communication with space division multiple access, and a sensor node uses a modulating retro-reflector for communication. Thus while a random sampling matrix is used to guide the establishment of links between head cluster and sensor nodes, the random linear projection is accomplished. To establish multiple links at the same time, an optical space division multiple access antenna is designed. It works in fixed beams switching mode and consists of optic lens with a large field of view（FOV）, fiber array on the focal plane which is used to realize virtual channels segmentation, direction of arrival sensor, optical matrix switch and controller. Based on the angles of nodes＇ laser beams, by dynamically changing the route, optical matrix switch actualizes the multi-beam full duplex tracking receiving and transmission. Due to the structure of fiber array, there will be several fade zones both in the focal plane and in lens＇ FOV. In order to lower the impact of fade zones and harmonize multibeam, a fiber array adjustment is designed. By theoretical, simulated and experimental study, the antenna＇s qualitative feasibility is validated.展开更多
文摘We know matrices and their transposes and we also know flip matrices. In my previous paper <i>Matrices-One Review</i>, I introduced transprocal matrix. Flip matrices are transpose of transprocal matrices. Now I would like to introduce water image of four matrices said above and properties of such matrices. Also we know, determinant of sum of matrices is not equal to sum of determinant of matrices. Why can’t we get equal value on addition side and additive side of determinant of matrix addition and subtraction? This question triggered me to find the reason. The basic algebra of mensuration gave ideas to retreat determinant of matrix addition and subtraction. I extent that ideas for matrices sum. Further, in 1812, French mathematician <b>Jacques Philippe Marie Binet</b> described how to multiply matrices. Matrices are defined on addition, subtraction and multiplication but not in division. By the inspiration of Binet, I would like to describe how to do divisions on matrices. This idea is derived from division of fractions. In division of fraction, reciprocal of divisor fraction multiplies with dividend fraction. I do the same in division on matrices with some modifications. By this way, we could find quotient matrix and remainder matrix which satisfy division algorithm. So we could say, determinant of division of dividend matrix and divisor matrix is equal to division of determinant of dividend matrix and determinant of divisor matrix.
基金supported by the National Natural Science Foundation of China(61372069)and the"111"Project(B08038)
文摘In order to apply compressive sensing in wireless sensor network, inside the nodes cluster classified by the spatial correlation, we propose that a cluster head adopts free space optical communication with space division multiple access, and a sensor node uses a modulating retro-reflector for communication. Thus while a random sampling matrix is used to guide the establishment of links between head cluster and sensor nodes, the random linear projection is accomplished. To establish multiple links at the same time, an optical space division multiple access antenna is designed. It works in fixed beams switching mode and consists of optic lens with a large field of view（FOV）, fiber array on the focal plane which is used to realize virtual channels segmentation, direction of arrival sensor, optical matrix switch and controller. Based on the angles of nodes＇ laser beams, by dynamically changing the route, optical matrix switch actualizes the multi-beam full duplex tracking receiving and transmission. Due to the structure of fiber array, there will be several fade zones both in the focal plane and in lens＇ FOV. In order to lower the impact of fade zones and harmonize multibeam, a fiber array adjustment is designed. By theoretical, simulated and experimental study, the antenna＇s qualitative feasibility is validated.
