How Does the Length of a Kronecker Product Relate to Its Component Vectors?

Thread starter Dragonfall
Start date Sep 17, 2009
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Length Tensors Vector

In summary, the length of vector tensors is the magnitude or size of a vector tensor, calculated using the Pythagorean theorem. A longer length indicates a stronger or more intense vector, and it is always a positive value. This property is closely related to other fundamental properties of vector tensors and can be used to calculate various other properties.

Sep 17, 2009

Dragonfall

Suppose a, b are vectors in R^n, R^m resp. What can I say about the length of [tex]a\otimes b[/tex] wrt a and b?

You can think of [tex]\otimes[/tex] as the Kronecker product.

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Sep 19, 2009

Dragonfall

Anyone?

Sep 19, 2009

HallsofIvy

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Homework Helper

How do you define the "length" of a tensor?

Sep 19, 2009

Dragonfall

Euclidean length.

Related to How Does the Length of a Kronecker Product Relate to Its Component Vectors?

1. What is the definition of "length of vector tensors"?

The length of vector tensors refers to the magnitude or size of a vector tensor. It is a measurement of the overall strength or intensity of the vector tensor.

2. How is the length of vector tensors calculated?

The length of vector tensors is calculated using the Pythagorean theorem, which involves taking the square root of the sum of the squares of the vector's components. This calculation is also known as the vector's Euclidean norm.

3. What does a longer length of vector tensors indicate?

A longer length of vector tensors indicates a stronger or more intense vector. It can also suggest a larger magnitude or impact of the vector in a given situation.

4. Can the length of vector tensors be negative?

No, the length of vector tensors is always a positive value. This is because it is calculated by taking the square root of the sum of squared values, which cannot result in a negative number.

5. How does the length of vector tensors relate to other properties of vector tensors?

The length of vector tensors is one of the fundamental properties of vector tensors, along with direction and orientation. It is also closely related to the vector's magnitude and can be used to calculate other properties such as dot product and cross product.