language agnostic - What is Orthogonality? - Stack Overflow Orthogonality is the property that means "Changing A does not change B" An example of an orthogonal system would be a radio, where changing the station does not change the volume and vice-versa A non-orthogonal system would be like a helicopter where changing the speed can change the direction In programming languages this means that when you execute an instruction, nothing but that
linear algebra - What does orthogonality mean in function space . . . "Orthogonality" is a measure of how much two vectors have in common In an orthogonal basis, the vectors have nothing in common If this is the case, I can get a given vector's components in this basis easily because the inner product with one basis vector makes all other basis vectors in the linear combination go to zero
linear algebra - What is the difference between orthogonal and . . . You can think of orthogonality as vectors being perpendicular in a general vector space And for orthonormality what we ask is that the vectors should be of length one So vectors being orthogonal puts a restriction on the angle between the vectors whereas vectors being orthonormal puts restriction on both the angle between them as well as the length of those vectors These properties are
What really is orthogonality? - Mathematics Stack Exchange So orthogonality seems a ''coordinate dependent'' concept The question is: is my reasoning correct? And, if yes, what make the usual standard basis so special that we chose such basis for the usual definition of orthogonality? I add something to better illustrate my question
What does it mean for two matrices to be orthogonal? So, the problem is that I can understand the meaning of orthogonality between two vectors, they are just "lines" perpendicular to each other, but I can not physically perceive what orthogonality means for matrices (like a $3\times 3$ one) I mean if vectors are like lines in space, those being orthogonal is an easy concept to visualize
theory - Is Java orthogonal? - Stack Overflow Orthogonality is feature of your design independent of the language Sure some language make it easier for you to have an orthogonal design for your system but you shouldn't focus on a specific language to keep your system's design as orthogonal as possible
Row orthogonality vs Column orthogonality - Mathematics Stack Exchange One may say that if we know all the irreducible characters except one character $\psi$, then we can get it from column-orthogonality But, it is much easier to cover $\psi$ from the remaining and the regular character than the column orthogonality This raised question of practical use of column-orthogonality