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The convolution of two finite sequences is defined by extending the sequences to finitely supported functions on the set of integers. When the sequences are the coefficients of two polynomials, then the coefficients of the ordinary product of the two polynomials are the convolution of the original two
Matrix representation is a method used by a computer language to store column-vector matrices of more than one dimension in memory. Fortran and C use different schemes for their native arrays. Fortran uses "Column Major" , in which all the elements for a given column are stored contiguously in memory.
In addition to support for vectorized arithmetic and relational operations, these languages also vectorize common mathematical functions such as sine. For example, if x is an array, then y = sin (x) will result in an array y whose elements are sine of the corresponding elements of the array x. Vectorized index operations are also supported.
Pauli matrices: A set of three 2 × 2 complex Hermitian and unitary matrices. When combined with the I 2 identity matrix, they form an orthogonal basis for the 2 × 2 complex Hermitian matrices. Redheffer matrix: Encodes a Dirichlet convolution. Matrix entries are given by the divisor function; entires of the inverse are given by the Möbius ...
So for any two rows and two columns of a Monge array (a 2 × 2 sub-matrix) the four elements at the intersection points have the property that the sum of the upper-left and lower right elements (across the main diagonal) is less than or equal to the sum of the lower-left and upper-right elements (across the antidiagonal).
There are two kinds of matrices, viz. a refraction matrix describing the refraction at a lens surface, and a translation matrix, describing the translation of the plane of reference to the next refracting surface, where another refraction matrix applies. The optical system, consisting of a combination of lenses and/or reflective elements, is ...
Even if is not square, the two matrices and are both Hermitian and in fact positive semi-definite matrices. The conjugate transpose "adjoint" matrix A H {\displaystyle \mathbf {A} ^{\mathrm {H} }} should not be confused with the adjugate , adj ( A ) {\displaystyle \operatorname {adj} (\mathbf {A} )} , which is also sometimes called adjoint .
a = [3, 1, 5, 7] // assign an array to the variable a a [0.. 1] // return the first two elements of a a [.. 1] // return the first two elements of a: the zero can be omitted a [2..] // return the element 3 till last one a [[0, 3]] // return the first and the fourth element of a a [[0, 3]] = [100, 200] // replace the first and the fourth element ...