Linear Independence: Proving SIN(nx) is Indep.

Thread starter mkbh_10
Start date Sep 5, 2009
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Independence Linear Linear independence

In summary, linear independence is a concept in linear algebra that describes the relationship between vectors in a vector space. To prove linear independence, it must be shown that no vector in the set can be expressed as a linear combination of the other vectors, except by setting all coefficients to zero. SIN(nx) is a set of vectors related to linear independence because it represents sine waves with different frequencies. To prove that SIN(nx) is linearly independent, it must be shown that no linear combination of the sine waves can equal the zero vector. This has practical applications in fields such as signal processing and Fourier analysis.

Sep 5, 2009

mkbh_10

Show that the set of functions SIN(nx) where n=1,2,3... is linearly independent ?

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Sep 5, 2009

rootX

Can you add sin(n1 x) and sin(n2 x) to get sin(n3 x)

Sep 6, 2009

mkbh_10

nope , therefore linear independnce

Related to Linear Independence: Proving SIN(nx) is Indep.

1. What is linear independence?

Linear independence is a concept in linear algebra that describes the relationship between vectors in a vector space. It means that no vector in the set can be expressed as a linear combination of the other vectors in the set.

2. How do you prove linear independence?

To prove linear independence, you need to show that there is no way to create a linear combination of the vectors that equals the zero vector, except by setting all the coefficients to zero. This can be done through various methods, such as Gaussian elimination or using the definition of linear independence.

3. What is SIN(nx) and how is it related to linear independence?

SIN(nx) is a trigonometric function that represents a sine wave with a frequency of n. It is related to linear independence because it is a set of vectors in a vector space that can be used to prove linear independence.

4. Can you explain how to prove SIN(nx) is linearly independent?

To prove that SIN(nx) is linearly independent, you would need to show that there is no way to create a linear combination of the sine waves with different frequencies that equals the zero vector. This can be done by setting up a system of equations and showing that the only solution is when all the coefficients are equal to zero.

5. Why is proving SIN(nx) is linearly independent important?

Proving that SIN(nx) is linearly independent is important because it provides a concrete example of linear independence in action. It also has practical applications, such as in signal processing and Fourier analysis, where understanding linear independence is crucial for accurate calculations and predictions.