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In probability theory and statistics, a cross-covariance matrix is a matrix whose element in the i, j position is the covariance between the i-th element of a random vector and j-th element of another random vector. When the two random vectors are the same, the cross-covariance matrix is referred to as covariance matrix.
A tetrad is the association of a pair of homologous chromosomes (4 sister chromatids) physically held together by at least one DNA crossover. This physical attachment allows for alignment and segregation of the homologous chromosomes in the first meiotic division. In most organisms, each replicated chromosome (composed of two identical sisters ...
Noting that any identity matrix is a rotation matrix, and that matrix multiplication is associative, we may summarize all these properties by saying that the n × n rotation matrices form a group, which for n > 2 is non-abelian, called a special orthogonal group, and denoted by SO(n), SO(n,R), SO n, or SO n (R), the group of n × n rotation ...
Each homology class is an equivalence class over cycles and two cycles in the same homology class are said to be homologous. [6] A chain complex is said to be exact if the image of the (n+1)th map is always equal to the kernel of the nth map. The homology groups of X therefore measure "how far" the chain complex associated to X is from being ...
The cross-correlation matrix of two random vectors is a matrix containing as elements the cross-correlations of all pairs of elements of the random vectors. The cross-correlation matrix is used in various digital signal processing algorithms.
A pair of homologous chromosomes, or homologs, is a set of one maternal and one paternal chromosome that pair up with each other inside a cell during fertilization. Homologs have the same genes in the same loci , where they provide points along each chromosome that enable a pair of chromosomes to align correctly with each other before ...
The "fifth matrix" is not a proper member of the main set of four; it is used for separating nominal left and right chiral representations. The gamma matrices have a group structure, the gamma group , that is shared by all matrix representations of the group, in any dimension, for any signature of the metric.
Let H be a Hadamard matrix of order n.The transpose of H is closely related to its inverse.In fact: = where I n is the n × n identity matrix and H T is the transpose of H.To see that this is true, notice that the rows of H are all orthogonal vectors over the field of real numbers and each have length .