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Unit Matrix
A unit matrix is aninteger matrix consisting of all 1s. The
unit matrix is often denoted
, or
if
. Square unit matrices
havedeterminant 0 for
.
An
unit matrix can be generated in theWolfram Language asConstantArray[1,
m,n
].
Let
be acommutative ring with amultiplicative identity. Then the term "unit matrix" is also used to refer to an
square matrix
with entries in
for which there exists an
square matrix
such that
 |
with
is theidentity matrix (MacDuffee 1943, p. 27; Marcus and Minc 1988, p. 69; Marcus and Minc 1992, p. 42).
The term "unit matrix" is sometimes also used as a synonym foridentitymatrix (Akivis and Goldberg 1972, p. 71).
See also
Identity Matrix,UnimodularMatrix,Unitary MatrixExplore with Wolfram|Alpha
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References
Akivis, M. A. and Goldberg, V. V.An Introduction to Linear Algebra and Tensors. New York: Dover, 1972.Brenner, J. and Cummings, L. "The Hadamard Maximum Determinant Problem."Amer. Math. Monthly79, 626-630, 1972.MacDuffee, C. C.Vectors and Matrices. Washington, DC: Math. Assoc. Amer., 1943.Marcus, M. and Minc, H.Introduction to Linear Algebra. New York: Dover, 1988.Marcus, M. and Minc, H.A Survey of Matrix Theory and Matrix Inequalities. New York: Dover, 1992.Referenced on Wolfram|Alpha
Unit MatrixCite this as:
Weisstein, Eric W. "Unit Matrix." FromMathWorld--A Wolfram Resource.https://mathworld.wolfram.com/UnitMatrix.html