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Orthogonal  Having Equal Product From  Integral Functions ə

Title orthogonal
Text
Merriam-Webster's Collegiate Dictionary
or·thog·o·nal
 \\ȯr-ˈthä-gə-nəl\\ adjective
 ETYMOLOGY  Middle French, from Latin orthogonius, from Greek orthogōnios, from orth- + gōnia angle — more at 
-gon
 DATE  1612
1.
  a. intersecting or lying at right angles
  b. having perpendicular slopes or tangents at the point of intersection
      orthogonal curves
2. having a sum of products or an integral that is zero or sometimes one under specified conditions: as
  a. of real-valued functions : having the integral of the product of each pair of functions over a specific interval equal to zero
  b. of vectors : having the scalar product equal to zero
  c. of a square matrix : having the sum of products of corresponding elements in any two rows or any two columns equal to one if the rows or columns are the same and equal to zero otherwise : having a transpose with which the product equals the identity matrix
3. of a linear transformation : having a matrix that is orthogonal :preserving length and distance
4. composed of mutually orthogonal elements
    an orthogonal basis of a vector space
5. statistically independent
• or·thog·o·nal·i·ty 
 \\-ˌthä-gə-ˈna-lə-tē\\ noun
• or·thog·o·nal·ly 
 \\-ˈthä-gə-nəl-ē\\ adverb
English Etymology
orthogonal
  from Fr. orthogonal, from orthogone, from L.L. orthogonius, from Gk. orthogonios "right-angled," from ortho- "straight" (see ortho-) + gonia "angle," related to gony "knee" (see knee).
Webster's Third New International Dictionary, Unabridged
Search result show the entry is found in: orthogonal functions , or orthogonal projection , or orthogonal system , or orthogonal trajectory , or normal orthogonal

or·thog·o·nal
I. \(ˈ)ȯ(r)|thägənəl\ adjective
Etymology: Middle French, from Latin orthogonius orthogonal (from Greek orthogōnios, from orth- + -gōnios, from -gōnia angle) + Middle French -al — more at 
-gon
1. : lying or intersecting at right angles : 
rectangular
right-angled
 < wind and sea may displace the ship's center of gravity along three orthogonal axes — C.C.Shaw >
 < in orthogonal cutting, the cutting edge is perpendicular to the direction of tool travel — M.E.Merchant & Hans Ernst >
2. 
 a. : mutually perpendicular
  < two vector functions the integral of whose scalar product throughout space is zero are orthogonal >
 b. : completely independent
  < two statistical variables having zero correlation are orthogonal >
  < mental ability may be classified into several orthogonal … factors — O.D.Duncan >
• or·thog·o·nal·ly \-gənəlē, -gnəlē\ adverb
II. noun
(-s)
: an imaginary line at right angles to wave crests in oceanography
III. adjective
1. : having a sum of products or an integral that is zero or sometimes 1 under specified conditions: as 
 a. of real-valued functions : having the integral of the product of each pair of functions over a specific interval equal to zero 
 b. of vectors : having the scalar product equal to zero 
 c. of a square matrix : having the sum of products of corresponding elements in any two rows or any two columns equal to 1 if the rows or columns are the same and equal to zero otherwise : having a transpose with which the product equals the identity matrix 
2. of a linear transformation : having a matrix that is orthogonal :preserving length and distance 
3. : composed of mutually orthogonal elements 
 < an orthogonal basis of a vector space >

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