Linear Map — Illustration — Preservation of Scalar Multiplication: L(α·u) = α·L(u)

Step 1 of 7

Operator Definition

[L] : C²(I) ➜ C(I)

( L y )( x ) =

y″(x) + p(x) · y′(x) + q(x) · y(x)

Animation

Choose u:

Scalar α:

Speed

Operator Computation

1) Operator on any function:

L[y] = y″ + p(x)·y′ + q(x)·y

2) Computing L(α·u)

3) Computing α·L(u)

4) Linearity Identity — Scalar Extraction

L(α·u) = α·L(u)

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