Is the Matrix B Positive or Not?

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In summary, the author of a website states that a specific matrix is not positive. However, a different source defines a positive matrix as one with all elements greater than zero, causing a discrepancy. The confusion may arise from the fact that a nonnegative matrix, defined as having elements equal to or greater than zero, is not necessarily the same as a positive matrix.
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I haven't read the links, but zero is not greater than zero. So why would a matrix containing a zero be "positive"?
 
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From the wiki page,
A nonnegative matrix is a matrix in which all the elements are equal to or greater than zero.
A positive matrix is a matrix in which all the elements are greater than zero.
Nonnegative isn't the same thing as positive.
 
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:oops: Oops. Thanks, Stephen Tashi and Mark44. I should get more sleep...
 
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As a scientist, it is important to be precise and accurate in our use of language. In this case, the discrepancy arises from the fact that there are different definitions of a "positive" matrix in mathematics.

In the context of linear algebra, a positive matrix is defined as a square matrix where all the elements are positive. This aligns with the definition you found on Wikipedia. However, in the context of optimization and convex analysis, a positive matrix is defined as a square matrix where all the elements are non-negative. This is the definition used in the website you referenced.

It is important to note that both definitions are valid and useful in their respective fields. It is simply a matter of different conventions and contexts.

In this case, the matrix B is not positive in the context of optimization and convex analysis, since it contains some zero elements. However, it is non-negative in this context, which means it can still be useful for certain applications. It is important to clarify which definition is being used in order to avoid confusion or discrepancies.
 

FAQ: Is the Matrix B Positive or Not?

Why isn't this positive?

1. Why do some things have a negative charge?

The concept of positive and negative charge is relative, meaning something can only have a negative charge if there is something else with a positive charge to compare it to. In atoms, protons have a positive charge while electrons have a negative charge. The number of each determines the overall charge of an atom.

2. Why do some chemical reactions release energy while others require energy?

Chemical reactions involve the transfer of electrons between atoms. When electrons are transferred from a higher energy state to a lower energy state, energy is released. This is seen as a positive change in energy. On the other hand, if electrons are transferred from a lower energy state to a higher energy state, energy is required, resulting in a negative change in energy.

3. Why do some substances have a positive charge while others have a negative charge?

The charge of a substance depends on the balance of positive and negative particles within it. If a substance has more protons than electrons, it will have a net positive charge. If it has more electrons than protons, it will have a net negative charge. The overall charge of a substance can also be influenced by external factors, such as the presence of other charged particles.

4. Why do some types of radiation have a positive charge?

Radiation can have a positive charge if it is made up of particles that have a net positive charge. For example, alpha particles, which are made up of two protons and two neutrons, have a net positive charge. This is because they have more protons than electrons, resulting in a net positive charge.

5. Why do some substances have a neutral charge?

Some substances have a neutral charge because they have an equal number of positive and negative particles, resulting in a net charge of zero. This can occur when atoms share or transfer electrons, resulting in a balanced distribution of charges. In some cases, substances may also have a neutral charge due to the cancellation of positive and negative charges within the substance.

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