Identity Matrix

Author

Eric W. Weisstein
March 9, 2003

This notebook downloaded from http://mathworld.wolfram.com/notebooks/LinearAlgebra/IdentityMatrix.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/IdentityMatrix.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Code

MatrixEquation[r_,n_]:=Module[{m=Array[a,{n,n}]},
Dot@@Table[#,{r}]&[m]
]

MatrixRoot[r_,n_]:=Module[{m=Array[a,{n,n}]},
m/.Solve[Dot@@Table[#,{r}]&[m]==IdentityMatrix[n],Flatten[m]]
]

Mathematica Command

MatrixForm/@Table[IdentityMatrix[n],{n,4}]

Square Root Matrices

2×2

MatrixForm/@MatrixEquation[2,2]

MatrixForm/@MatrixRoot[2,2]

MatrixForm/@(#.#&/@MatrixRoot[2,2])

#.#&[(({{-d, ((1-(d^2))/c)}, {c, d}}))]

Solve[(1-d^2)/c==x,c]

#.#&[(({{-d, x}, {((1-(d^2))/x), d}}))]

Cube Root

2×2

MatrixForm/@MatrixRoot[3,2]

MatrixForm/@Simplify/@(#.#.#&/@MatrixRoot[3,2])