Sentence examples for and matrices will be from inspiring English sources

A variety of norms on real-valued vectors and matrices will be used.

In these notes, vectors will be denoted by bold lowercase letters, and matrices will be denoted by bold uppercase letters.

Finally, we draw the conclusions in Section 6. Notation: Throughout this paper, vectors and matrices will be represented by boldfaced lowercase and uppercase letters (e.g., x and X), respectively.

In particular, graphics/visuals in the form of maps, pictures, calendars and matrices will be utilised to describe their current situation and understandings.

The adhesion between the fibre and matrix will be investigated.

In terms of the deterministic dynamics Eq. (2), the solution x (t) will be replaced by its fixed point value x *, and so the A and B matrices will be independent of time.

Taking into consideration that real mode shapes satisfy the mass normalization condition as φ i T M φ i  = 1, the mass and stiffness matrices will be determined via measured modal data as follows: M x = ∑ i = 1 N φ x i φ x i T - 1 (6) K x = M x ∑ i = 1 N ω x i 2 φ x i φ x i T M x (7).

However, for data sets as large as that used in the present study (23 subjects*4 days*480 minutes = 44160 observations), computations with very large variance and covariance matrices will be involved.

However, since this will mean that the clocks, ZWD, and gradients are estimated for every epoch, the number of parameters will be very large and thus the design and normal equation matrices will be huge, hence the inversion may be time consuming.

For A ∈ ℝ n × m, we write A ≽ 0 ≼ 0, ≻ 0, and ≺ 0 to indicate that all elements of matrix A are nonnegative (non-positive, positive, and negative) and the notation of matrices will be used throughout this brief: A = [a lg ] and A i = [ a l g ( i ) ] ⋅.

Spatial organization of two chromophores using small and stable protein matrices will be promising toward the construction of an artificial light-harvesting complex by protein engineering.