Page 512 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Appen. C.2 Matrices 499

Unit matrix. The unit matrix
1 0 0
I = 0 1 0
0 0 1
is a square matrix in which the diagonal elements from the top left to the bottom
right are unity with all other elements equal to zero.
Diagonal matrix. A square matrix having elements a^^ along the diagonal
with all other elements equal to zero is a diagonal matrix.
«11 0 0
0 «22 0
0 0 «33

Transpose. The transpose of a matrix A is one in which the rows and
columns are interchanged. For example,
■«11 ^21
A - «12 ^22
^22 ^23
«13 ^23
The transpose of a column matrix is a row matrix.

- = ['^l-^2'^3]

-
Minor. A minor M^ of a matrix A is formed by deleting the iih row and
the jth column from the determinant of the original matrix.
«11 «12 «13
Let A «21 «22 «23
«31 «32 «33
«11 «12 «13
M. «21 «22 «23 = «21 ^23
«31
«31 «32 «33
Cofactor. The cofactor is equal to the signed minor ( - From
the previous example,

Adjoint matrix. An adjoint matrix of a square matrix A is a transpose of
the matrk of cofactors of A.