Matrix of ones

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

J_2=\begin{pmatrix}
1 & 1 \\
1 & 1 
\end{pmatrix};\quad
J_3=\begin{pmatrix}
1 & 1 & 1 \\
1 & 1 & 1 \\
1 & 1 & 1
\end{pmatrix};\quad
J_{2,5}=\begin{pmatrix}
1 & 1 & 1 & 1 & 1 \\
1 & 1 & 1 & 1 & 1 
\end{pmatrix}.\quad

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[edit]

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

References[edit]

  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. ^ a b 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 .