Unit Matrix
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 ConstantArray [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
| AB=BA=I_n, |
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 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. 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.Referenced on Wolfram|Alpha
Unit MatrixCite this as:
Weisstein, Eric W. "Unit Matrix." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/UnitMatrix.html