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In mathematics, a matrix of ones is a matrix where every element is equal to one. Examples of standard notation are given below:## Properties

For an n×n matrix of ones U, the following properties hold:## References

- $J\_2=begin\{pmatrix\}$

In special contexts, the term unit matrix is used as a synonym for "matrix of ones This is done whenever it is clear that "unit matrix" does not refer to the identity matrix.

- The trace of U is n, and the determinant is zero.
- The rank of U is 1 and the eigenvalues are n (once) and 0 (n-1 times).
- $U^k\; =\; n^\{k-1\}\; U,\; mbox\{\; for\; \}\; k=1,2,ldots.,$
- The matrix $tfrac1n\; U$ is idempotent. This is a simple corollary of the above.
- $operatorname\{exp\}(U)\; =\; I\; +\; frac\{\; e^n-1\}\{n\}\; U,$ where exp(U) is the matrix exponential.
- Multiplication by U with the Hadamard product is the identity operator.

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Last updated on Monday March 17, 2008 at 02:53:05 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Monday March 17, 2008 at 02:53:05 PDT (GMT -0700)

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