Linear Transformation

Question 1

Another name of Linear Transformation

Answer 1

Linear Map

Question 2

Definition of Linear Transformation

Answer 2

It is mapping from vector space to vector space

Question 3

Notation of Linear Transformation

Answer 3

T: V₁→V₂
Here V₁, V2 are vector spaces

Question 4

T: V₁→V₂
What are V₁, V₂ here

Answer 4

V₁, V₂ are vector spaces
V₁ is the domain of the transformation
V₂ is the codomain of the transformation

Question 5

Can we say linear transformation is mapping from subspace to subspace . Give reason for your answer

Answer 5

Yes we can say linear transformation is mapping from subspace to subspace because subspace is also vector space

Question 6

AX = Y
Convert it into linear transformation notation

Answer 6

A: X→Y

Question 7

A: X→Y
Explain

Answer 7

A is linear transformation matrix which transform the vector X into Vector Y

Question 8

Projection

Answer 8

T is the projection which projects the higher dimension vector space (vector) into lower vector space (vector)

Question 9

Answer 9

Question 10

Answer 10

Question 11

If Aₙₓₙ is projection matrix then

Answer 11

Question 12

If A is projection matrix, what it tells about A

Answer 12

A is idempotent and symmetric matrix

Question 13

Projection matrix onto θ-line

Answer 13