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The direction of vector rotation is counterclockwise if θ is positive (e.g. 90°), and clockwise if θ is negative (e.g. −90°) for ().Thus the clockwise rotation matrix is found as
Boschloo's test is a statistical hypothesis test for analysing 2x2 contingency tables. It examines the association of two Bernoulli distributed random variables and is a uniformly more powerful alternative to Fisher's exact test. It was proposed in 1970 by R. D. Boschloo. [1]
The following is a general formula that applies to almost any 2 × 2 matrix. [1] Let the given matrix be = (), where A, B, C, and D may be real or complex numbers. Furthermore, let τ = A + D be the trace of M, and δ = AD − BC be its determinant.
Likewise, inverses of triangular matrices are algorithmically easier to calculate. The Gaussian elimination is a similar algorithm; it transforms any matrix to row echelon form . [ 51 ] Both methods proceed by multiplying the matrix by suitable elementary matrices , which correspond to permuting rows or columns and adding multiples of one row ...
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 linear algebra, linear transformations can be represented by matrices.If is a linear transformation mapping to and is a column vector with entries, then there exists an matrix , called the transformation matrix of , [1] such that: = Note that has rows and columns, whereas the transformation is from to .
If the determinant of A and the inverse of A have already been computed, the matrix determinant lemma allows rapid calculation of the determinant of A + uv T, where u and v are column vectors. Charles Dodgson (i.e. Lewis Carroll of Alice's Adventures in Wonderland fame) invented a method for computing determinants called Dodgson condensation ...
Wolfgang Pauli (1900–1958), c. 1924. Pauli received the Nobel Prize in Physics in 1945, nominated by Albert Einstein, for the Pauli exclusion principle.. In mathematical physics and mathematics, the Pauli matrices are a set of three 2 × 2 complex matrices that are traceless, Hermitian, involutory and unitary.