Matrix of ones

In mathematics, a matrix of ones or all-ones matrix is a matrix over the real numbers where every element is equal to one.[1] Examples of standard notation are given below:

Some sources call the all-ones matrix the unit matrix,[2] but that term may also refer to the identity matrix, a different matrix.

Properties

For an n×n matrix of ones J, the following properties hold:

References

  1. Horn, Roger A.; Johnson, Charles R. (2012), "0.2.8 The all-ones matrix and vector", Matrix Analysis, Cambridge University Press, p. 8, ISBN 9780521839402.
  2. Weisstein, Eric W. "Unit Matrix". MathWorld.
  3. Stanley, Richard P. (2013), Algebraic Combinatorics: Walks, Trees, Tableaux, and More, Springer, Lemma 1.4, p. 4, ISBN 9781461469988.
  4. Stanley (2013); Horn & Johnson (2012), p. 65.
  5. 1 2 Timm, Neil H. (2002), Applied Multivariate Analysis, Springer texts in statistics, Springer, p. 30, ISBN 9780387227719.
  6. Smith, Jonathan D. H. (2011), Introduction to Abstract Algebra, CRC Press, p. 77, ISBN 9781420063721.
  7. Godsil, Chris (1993), Algebraic Combinatorics, CRC Press, Lemma 4.1, p. 25, ISBN 9780412041310.
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