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Several sets of orthogonal functions have become standard bases for approximating functions. For example, the sine functions sin nx and sin mx are orthogonal on the interval x ∈ ( − π , π ) {\displaystyle x\in (-\pi ,\pi )} when m ≠ n {\displaystyle m\neq n} and n and m are positive integers.
The line segments AB and CD are orthogonal to each other. In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity.Whereas perpendicular is typically followed by to when relating two lines to one another (e.g., "line A is perpendicular to line B"), [1] orthogonal is commonly used without to (e.g., "orthogonal lines A and B").
We say that functions and are orthogonal if their inner product (equivalently, the value of this integral) is zero: f , g w = 0. {\displaystyle \langle f,g\rangle _{w}=0.} Orthogonality of two functions with respect to one inner product does not imply orthogonality with respect to another inner product.
Example of orthogonal factorial design Orthogonality concerns the forms of comparison (contrasts) that can be legitimately and efficiently carried out. Contrasts can be represented by vectors and sets of orthogonal contrasts are uncorrelated and independently distributed if the data are normal.
This glossary of biology terms is a list of definitions of fundamental terms and concepts used in biology, the study of life and of living organisms.It is intended as introductory material for novices; for more specific and technical definitions from sub-disciplines and related fields, see Glossary of cell biology, Glossary of genetics, Glossary of evolutionary biology, Glossary of ecology ...
In evolutionary biology, function is the reason some object or process occurred in a system that evolved through natural selection. That reason is typically that it achieves some result, such as that chlorophyll helps to capture the energy of sunlight in photosynthesis .
n=0 of orthogonal polynomials is defined by the relations = , , = . In other words, the sequence is obtained from the sequence of monomials 1, x, x 2, … by the Gram–Schmidt process with respect to this inner product.
This definition can be formalized in Cartesian space by defining the dot product and specifying that two vectors in the plane are orthogonal if their dot product is zero. Similarly, the construction of the norm of a vector is motivated by a desire to extend the intuitive notion of the length of a vector to higher-dimensional spaces.