Given four complex matrices $A$‎, ‎$B$‎, ‎$C$ and $D$ where $Ainmathbb{C}^{ntimes n}$‎ ‎and $Dinmathbb{C}^{mtimes m}$ and let the matrix $left(begin{array}{cc}‎ A & B ‎ C & D‎ end{array} right)$ be a normal matrix and‎ assume that $lambda$ is a given complex number‎ ‎that is not eigenvalue of matrix $A$‎. ‎We present a method to calculate the distance norm (with respect to 2-norm) from $D$‎ to ...

In this paper, we handle the problem of human action recognition by combining covariance matrices as local spatio-temporal (ST) descriptors and local ST features extracted densely from action video. Unlike traditional methods that separately utilizing gradient-based feature and optical flow-based feature, we use covariance matrix to fuse the two types of feature. Since covariance matrices are S...

Each nonnegative matrix, ( : , 1,.., ) ij W w i j n   , is a possible spatial weight matrix summarizing spatial relations between n spatial units. Here each spatial weight, ij w , typically reflects the “spatial influence” of unit j on unit i . Following standard convention, we here exclude “self influence” by assuming that 0 ii w  for all 1,.., i n  (so that W has a zero diagonal). The fol...

In this work we study in detail the conditions under which the stiffness matrix of a spatial system can be transformed into block-diagonal and diagonal form. That is the existence of a coordinate frame in which the stiffness matrix takes on these simple forms. The consequences of a block-diagonal or diagonal stiffness matrix for the invariants of the system, principal screws, von Mises’ invaria...