Search results
Results From The WOW.Com Content Network
(Similarly, here, "basis" can equivalently be replaced with either "linearly independent set" or "spanning set") The determinant of A is nonzero: det A ≠ 0 . (In general, a square matrix over a commutative ring is invertible if and only if its determinant is a unit (i.e. multiplicatively invertible element) of that ring.
The transform in the original basis is found to be the product of three easy-to-derive matrices. In effect, the similarity transform operates in three steps: change to a new basis (P), perform the simple transformation (S), and change back to the old basis (P −1).
The inverse Gaussian distribution is a two-parameter exponential family with natural parameters −λ/(2μ 2) and −λ/2, and natural statistics X and 1/X.. For > fixed, it is also a single-parameter natural exponential family distribution [4] where the base distribution has density
This happens if and only if A has n eigenvectors which constitute a basis for C n. In this case, V can be chosen to be the matrix with the n eigenvectors as columns, and thus a square root of A is = , where S is any square root of D. Indeed,
for all indices and , where is the element in the -th row and -th column of , and the overline denotes complex conjugation.. Skew-Hermitian matrices can be understood as the complex versions of real skew-symmetric matrices, or as the matrix analogue of the purely imaginary numbers. [2]
In vector calculus, the Jacobian matrix (/ dʒ ə ˈ k oʊ b i ə n /, [1] [2] [3] / dʒ ɪ-, j ɪ-/) of a vector-valued function of several variables is the matrix of all its first-order partial derivatives.
In mathematics, the conjugate transpose, also known as the Hermitian transpose, of an complex matrix is an matrix obtained by transposing and applying complex conjugation to each entry (the complex conjugate of + being , for real numbers and ).
Hexadecimal (also known as base-16 or simply hex) is a positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbols, hexadecimal uses sixteen distinct symbols, most often the symbols "0"–"9" to represent values 0 to 9 and "A"–"F" to represent values from ten to fifteen.