linear transformation A transformation in which the origin of reference frame doesn't change and new cordinate is obtained is linear function of old coordinate i.e. X'=aX+bY and Y'=cX+bY is called linear transformation. In such stated transformation, the straight line remains straight.

2016年1月23日 · By definition, an affine transformation does preserve the other underlying properties of the original linear function, because it is a "parallel" shift That's why it's considered a "linear" transformation, even though the term is, in fact, slightly misleading in this context.

2021年3月12日 · First: linear transformation vs. matrix. Matrices. A matrix is a rectangular array, in the context of linear algebra the entries are always elements of the ground field (in your case, probably either the real numbers or the complex numbers).

2012年12月27日 · Only a subset of linear transformations also preserves angles. Orthogonal transformations preserve length and angles and can easily be characterized. If you want to drop the length condition then also stretching with the same factor along all coordinate axes is allowed.

This is a linear transformation. The operator defining this transformation is an angle rotation. Consider a dilation of a vector by some factor. That is also a linear transformation. The operator this particular transformation is a scalar multiplication. The operator is sometimes referred to as what the linear transformation exactly entails ...

2017年9月2日 · A general transformation doesn't preserve linear indipendency. The statement is true if and only if the transformation is bijective.

2016年12月5日 · Proof that a linear transformation is continuous. Ask Question Asked 11 years, 8 months ago.

I'm working on a problem from Dummit & Foote's Abstract Algebra and I can't figure out what exactly I'm being asked to prove. I hate to ask this here, because it seems that I should've been abl...

2015年10月31日 · $\begingroup$ The final part of your answer is slightly confusingly worded. It would be more correct to say that the linear transformation can be represented by different matrices depending on the choice of basis (you can even choose a different basis for the domain than for the codomain), but that in some (not all) vector spaces you have a standard basis that …

Recently, I am struglling with the difference between linear transformation and affine transformation. Are they the same ? I found an interesting question on the difference between the functions. ...