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A vector-valued function, also referred to as a vector function, is a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors. The input of a vector-valued function could be a scalar or a vector (that is, the dimension of the domain could be 1 or greater than 1); the ...
Interval vector, in musical set theory, an array that expresses the intervallic content of a pitch-class set; Probability vector, in statistics, a vector with non-negative entries that sum to one. Random vector or multivariate random variable, in statistics, a set of real-valued random variables that may be correlated.
Such an equivalence class is called a vector, more precisely, a Euclidean vector. [13] The equivalence class of (A, B) is often denoted . A Euclidean vector is thus an equivalence class of directed segments with the same magnitude (e.g., the length of the line segment (A, B)) and same direction (e.g., the direction from A to B). [14]
The kinetic energy equations are exceptions to the above replacement rule. The equations are still one-dimensional, but each scalar represents the magnitude of the vector, for example, = + +. Each vector equation represents three scalar equations.
From this derivative equation, in the one-dimensional case it can be seen that the area under a velocity vs. time (v vs. t graph) is the displacement, s. In calculus terms, the integral of the velocity function v ( t ) is the displacement function s ( t ) .
A matrix difference equation is a difference equation in which the value of a vector (or sometimes, a matrix) of variables at one point in time is related to its own value at one or more previous points in time, using matrices. [1] [2] The order of the equation is the maximum time gap between any two indicated values of the variable vector. For ...
The first example of a vector space consists of arrows in a fixed plane, starting at one fixed point. This is used in physics to describe forces or velocities . [ 30 ] Given any two such arrows, v and w , the parallelogram spanned by these two arrows contains one diagonal arrow that starts at the origin, too.
The phrase "linear equation" takes its origin in this correspondence between lines and equations: a linear equation in two variables is an equation whose solutions form a line. If b ≠ 0, the line is the graph of the function of x that has been defined in the preceding section.