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An optical mask (3) based on a weighing matrix is used in the measurement of the spectrum of incoming light (4). Depending on the corresponding element of the matrix, the light is either absorbed, or passed to one of two intensity detectors (1,2). [6]
An example batch calculation may be demonstrated here. The desired glass composition in wt% is: 67 SiO 2, 12 Na 2 O, 10 CaO, 5 Al 2 O 3, 1 K 2 O, 2 MgO, 3 B 2 O 3, and as raw materials are used sand, trona, lime, albite, orthoclase, dolomite, and borax. The formulas and molar masses of the glass and batch components are listed in the following ...
Multiplication of two matrices is defined if and only if the number of columns of the left matrix is the same as the number of rows of the right matrix. That is, if A is an m × n matrix and B is an s × p matrix, then n needs to be equal to s for the matrix product AB to be defined.
It is possible to make the spatial weight matrix a function of 'distance class': [7] where denotes the 'distance class', for example =,,, … corresponding to first, second, third etc. neighbors. In this case, functions of the spatial weight matrix become distance class dependent.
For example, if A is a 3-by-0 matrix and B is a 0-by-3 matrix, then AB is the 3-by-3 zero matrix corresponding to the null map from a 3-dimensional space V to itself, while BA is a 0-by-0 matrix. There is no common notation for empty matrices, but most computer algebra systems allow creating and computing with them.
A matrix effect value of less than 100 indicates suppression, while a value larger than 100 is a sign of matrix enhancement. An alternative definition of matrix effect utilizes the formula: M E = 100 ( A ( e x t r a c t ) A ( s t a n d a r d ) ) − 100 {\displaystyle ME=100\left({\frac {A(extract)}{A(standard)}}\right)-100}
The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries = =. From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop:
Vandermonde matrix: A row consists of 1, a, a 2, a 3, etc., and each row uses a different variable. Walsh matrix: A square matrix, with dimensions a power of 2, the entries of which are +1 or −1, and the property that the dot product of any two distinct rows (or columns) is zero. Z-matrix: A matrix with all off-diagonal entries less than zero.