Properties of linear transformation - Linear Transformation
Properties of linear transformation
Lessons
Notes:
Recall from last chapter the 2 properties of :
1.
2.
where and are vectors in and is a scalar.
Now the properties of linear transformation are very similar. Linear transformation preserves the operations of vector addition/subtraction and scalar multiplication. In other words, If T is linear, then:
1.
2.
3.
We can even combine property 1 and 2 to show that:
where , are vectors and , are scalars. Note that if this equation holds, then it must be linear.
If you have more than 2 vectors and 2 scalars? What if you have p vectors and p scalars? Then we can generalize this equation and say that:
Again if this equation holds, then it must be linear.
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Intro Lesson
Properties of Linear Transformation Overview:
