Matrices in a sentence

Because operations like matrix multiplication, matrix inversion, and determinant calculation are simple on diagonal matrices, computations involving matrices are much simpler if we can bring the matrix to a diagonal form.

In 1907 Joseph Wedderburn showed that associative hypercomplex systems could be represented by matrices, or direct sums of systems of matrices.

Jones matrices The Jones matrices are operators that act on the Jones vectors defined above.

Mathematical formulation Throughout, italic non-bold capital letters are 4×4 matrices, while non-italic bold letters are 3×3 matrices.

Matrices A square matrix with entries in a field is invertible (in the set of all square matrices of the same size, under matrix multiplication ) if and only if its determinant is different from zero.

Matrices main A typical matrix Matrices are a useful notion to encode linear maps.

Of matrices One can define a division operation for matrices.

One convenient choice is given by the Pauli matrices : : This map gives an injective algebra homomorphism from to the set of 2 × 2 complex matrices.

One is to use 2 × 2 complex matrices, and the other is to use 4 × 4 real matrices.

Some transformations may have image equal to the whole codomain (in this case the matrices with rank 2 ) but many do not, instead mapping into some smaller subspace (the matrices with rank 1 or 0 ).

The geometric description of the multiplication of complex numbers can also be expressed in terms of rotation matrices by using this correspondence between complex numbers and such matrices.

These are 2 2 matrices with complex entries, and the two-component complex column vectors on which these matrices act by matrix multiplication are the spinors.

The sum and product of two such matrices is again of this form, and the sum and product of complex numbers corresponds to the sum and product of such matrices.

This makes them slightly a-typical gamma matrices because in addition to their anti commutation relation they also satisfy commutation relations and the two-component complex column vectors on which these matrices act are spinors.

To do this, he replaced the Fourier expansions for the spatial coordinates by matrices, matrices which corresponded to the transition coefficients in the virtual oscillator method.

Using 4 × 4 real matrices, that same quaternion can be written as : where the skew-symmetric matrices are not unique.

While matrices were used in these cases, the algebra of matrices with their multiplication did not enter the picture as they did in the matrix formulation of quantum mechanics.

Kumar, who joined Kala Bhavana as a student the same year that Kar joined as faculty, said that Kar introduced new materials as matrices for printmaking.

The vocations are critical to a country’s standard of living, and quality of life matrices.

And, most important, they can own stocks that institutions can't because those stocks are too small or too illiquid or too overvalued in traditional matrices that may turn out to be silly a few years from now.