Lesson plan
Jacket matrix
In mathematics, a jacket matrix is a square symmetric matrix A= (a_{ij}) of order n if its entries are non-zero and real, complex, or from a finite field, and : \ AB=BA=I_n where I n is the identity matrix, and : \ B ={1 \over n}(a_{ij}^{-1})^T. where T denotes the transpose of the matrix. In other words, the inverse of a jacket matrix is determined by its element-wise or block-wise inverse. The definition above may also be expressed as: : \forall u,v \in \{1,2,\dots,n\}:~a_{iu},a_{iv} \neq 0, ~~~~ \sum_{i=1}^n a_{iu}^{-1}\,a_{iv} = \begin{cases} n, & u = v\\ 0, & u \neq v \end{cases} The jacket matrix is a generalization of the Hadamard matrix; it is a diagonal block-wise inverse matrix.
Article summary
In mathematics, a jacket matrix is a square symmetric matrix A= (a_{ij}) of order n if its entries are non-zero and real, complex, or from a finite field, and : \ AB=BA=I_n where I n is the identity matrix, and : \ B ={1 \over n}(a_{ij}^{-1})^T. where T denotes the transpose of the matrix. In other words, the inverse of a jacket matrix is determined by its element-wise or block-wise inverse. The definition above may also be expressed as: : \forall u,v \in \{1,2,\dots,n\}:~a_{iu},a_{iv} \neq 0, ~~~~ \sum_{i=1}^n a_{iu}^{-1}\,a_{iv} = \begin{cases} n, & u = v\\ 0, & u \neq v \end{cases} The jacket matrix is a generalization of the Hadamard matrix; it is a diagonal block-wise inverse matrix.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
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- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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