Product of column and row vectors

Thread starter RussianAnswer
Start date Jan 11, 2008
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Column Product Row Vectors

In summary, a product of column and row vectors is a mathematical operation that involves multiplying the elements of a column vector with the corresponding elements of a row vector to obtain a single value. This is calculated using the dot product or scalar product method and has the properties of being commutative, associative, and distributive. It is commonly used in scientific research to represent and calculate quantities in various fields. This operation can be applied to vectors of any size as long as the number of elements in the column vector is equal to the number of elements in the row vector, known as the compatibility condition.

Jan 11, 2008

RussianAnswer

Hi All,

I need to multiply column and row vectors but not sure that I am doing this right (on the picture below):

http://img244.imageshack.us/img244/6222/35459606ye4.th.jpg

Could you check it and correct if necessary? Thank you.

Last edited by a moderator: May 3, 2017

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Jan 11, 2008

rs1n

It is correct.

1. What is a product of column and row vectors?

A product of column and row vectors is a mathematical operation that results in a single value by multiplying the elements of a column vector with the corresponding elements of a row vector.

2. How is a product of column and row vectors calculated?

To calculate the product of column and row vectors, we use the dot product or scalar product method, where we multiply each element of the first vector with the corresponding element of the second vector and then sum up all the products.

3. What are the properties of a product of column and row vectors?

The product of column and row vectors is commutative, associative, and distributive, which means that the order of multiplication does not matter, the grouping of vectors does not affect the result, and we can distribute the product over addition and subtraction.

4. How is a product of column and row vectors used in scientific research?

In scientific research, the product of column and row vectors is used in various fields such as physics, engineering, and economics to represent and calculate quantities such as force, displacement, and profit.

5. Can a product of column and row vectors be applied to vectors of any size?

Yes, a product of column and row vectors can be applied to vectors of any size as long as the number of elements in the column vector is equal to the number of elements in the row vector. This is known as the compatibility condition for vector multiplication.