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matqkks
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Can we compare matrices?
If A-B>0 is positive definite, can we say A>B?
If A-B>0 is positive definite, can we say A>B?
Yes, this is valid notation. This definition of ##>## gives us a strict partial ordering on the set of ##N\times N## matrices. Similarly, you can define ##A \geq B## if ##A - B## is positive semidefinite.matqkks said:Can we compare matrices?
If A-B>0 is positive definite, can we say A>B?
Both A-B>0 and A>B are comparisons between two matrices, but they have different meanings. A-B>0 means that the elements in matrix B are all smaller than the corresponding elements in matrix A. On the other hand, A>B means that all elements in matrix A are greater than the corresponding elements in matrix B.
No, A-B>0 and A>B cannot be true at the same time. If A-B>0 is true, it means that the elements in matrix B are smaller than those in matrix A, which contradicts A>B where the elements in matrix A must be greater than those in matrix B.
Comparing matrices allows us to determine the relationship and differences between two sets of data. It can help us identify patterns, similarities, and differences between different matrices.
Yes, there are limitations to comparing matrices. The matrices must have the same dimensions in order to be compared. Additionally, the matrices must contain numerical data, as comparisons cannot be made with non-numerical data.
Comparing matrices can be useful in scientific research in various ways. It can help identify trends and patterns in data, aid in data analysis, and provide insights into relationships between different variables. It can also aid in making predictions and drawing conclusions based on the data being compared.