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Quaternion multiplication and matrix multiplication is also noncommutative.
In 2013, several verifiable and secure outsourcing protocols for matrix multiplication and matrix inversion were proposed in [22].
Consider the algebra, (mathbb{A}=M_{2times2}(mathbb{R})), of all (2 timatricestrices with usual operations of addition, scalar multiplication, and matrix multiplication.
Consider the algebra, (mathbb{A}=M_{2times2}(mathbb{R})), of all (2 timatricestrices with the usual operations of addition, scalar multiplication, and matrix multiplication.
Note that (Ξ t Ξ′ t + αI)−1 is the most time-consuming process in Eq.18, which involves matrix multiplication and matrix inversion.
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Looking at the expression given in (34), one can notice that the derivative is calculated using matrix multiplications and matrix inversions with dimensions N×N.
For example, when the size of is, the number of calculations involved in matrix multiplication is, and matrix inversion is (referring to (9), (10), and Table 1).
In sharp contrast to the multiplication and even matrix operations, only the exclusive OR operation will be required in both the encoding and decoding processes [26], making the LT code attractive to some low-complexity applications.
If we model the conformal array based on the Euler angle, three matrix multiplications and one matrix transposition are required for each element.
Towards this end we study the performance of some dense matrix computations such as matrix multiplication, LU decomposition and matrix inversion.
If the patient's own cells are used to initiate and drive the physiological processes of cell multiplication and differentiation, extracellular matrix production, and creation of tissue architecture, the potential for growing an immunologically matched implant exists.
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