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## Do linear transformations preserve basis?

However, the **linear transformation itself remains unchanged, independent of basis choice**. … We can also establish a bijection between the linear transformations on n n n-dimensional space V V V to m m m-dimensional space W W W.

## Do linear transformations preserve the origin?

Translation is an affine transformation, but not a linear transformation (**notice it does not preserve the origin**). Consequently, when you combine it with the rest of operations (by using augmented transformation matrices, for example, which is common practice in game development) you lose commutativity.

## Do linear transformations preserve distance?

[2.15] (Preserving distance) A linear transformation L **preserves distance if and only if the distance between any pair of points is equal to the distance between their images**.

## Do linear transformation preserves orthogonality?

Yes, **reflection** obviously preserves the LENGTH of every vector, so by the theorem, this means reflection is an orthogonal transformation. 4.

## Is linear operator preserve dependence?

Let T:V→W be a linear transformation. (1) First, we know that any linear transformation is linearly dependency preserving, namely for every S⊆V, if S is L.D. (linearly dependent), then T(S) is L.D..

## What is a one to one linear transformation preserves?

Linear Transformations

If a linear transformation is one-to-one, then **the image of every linearly independent subset of the domain is linearly independent**. A linear transformation is onto if every vector in the codomain is the image of some vector from the domain.

## What are the properties of linear transformation?

Properties of Linear Transformationsproperties Let T:**Rn↦R**m be a linear transformation and let →x∈Rn. T preserves the negative of a vector: T((−1)→x)=(−1)T(→x). Hence T(−→x)=−T(→x). T preserves linear combinations: Let →x1,…,→xk∈Rn and a1,…,ak∈R.

## What is the nullity of a linear transformation?

The nullity of a linear transformation is **the dimension of the kernel**, written nulL=dimkerL. Let L:V→W be a linear transformation, with V a finite-dimensional vector space.

## What makes a function a linear transformation?

A linear transformation (or a linear map) is a function **T:Rn→Rm** that satisfies the following properties: T(x+y)=T(x)+T(y)

## Do translations preserve angle measures?

Rotations, translations, reflections, and dilations all **preserve** angle measure.

## What transformation does not preserve area?

**Reflection** does not preserve orientation. Dilation (scaling), rotation and translation (shift) do preserve it.