Unit Matrix

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A unit matrix is an integer matrix consisting of all 1s. The 👁 m×n
unit matrix is often denoted 👁 J_(mn)
, or 👁 J_n
if 👁 m=n
. Square unit matrices 👁 J_n
have determinant 0 for 👁 n>=2
.

An 👁 m×n
unit matrix can be generated in the Wolfram Language as [1, 👁 {
m, n👁 }
].

Let 👁 R
be a commutative ring with a multiplicative identity. Then the term "unit matrix" is also used to refer to an 👁 n×n
square matrix 👁 A
with entries in 👁 R
for which there exists an 👁 n×n
square matrix 👁 B
such that

with 👁 I_n
is the identity 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 for identity matrix (Akivis and Goldberg 1972, p. 71).

See also

Identity Matrix, Unimodular Matrix, Unitary Matrix

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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. Monthly 79, 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.

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Unit Matrix

Cite this as:

Weisstein, Eric W. "Unit Matrix." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/UnitMatrix.html

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