A square matrix A is idempotent if A^2 = A. It's really simple
Since the columns of AT equal the rows of A by definition, they also span the same space, so yes, they are equivalent.
Hermitian matrix defined:If a square matrix, A, is equal to its conjugate transpose, A†, then A is a Hermitian matrix.Notes:1. The main diagonal elements of a Hermitian matrix must be real.2. The cross elements of a Hermitian matrix are complex numbers having equal real part values, and equal-in-magnitude-but-opposite-in-sign imaginary parts.
A matrix A is orthogonal if itstranspose is equal to it inverse. So AT is the transpose of A and A-1 is the inverse. We have AT=A-1 So we have : AAT= I, the identity matrix Since it is MUCH easier to find a transpose than an inverse, these matrices are easy to compute with. Furthermore, rotation matrices are orthogonal. The inverse of an orthogonal matrix is also orthogonal which can be easily proved directly from the definition.
Skew-Hermitian matrix defined:If the conjugate transpose, A†, of a square matrix, A, is equal to its negative, -A, then A is a skew-Hermitian matrix.Notes:1. The main diagonal elements of a skew-Hermitian matrix must be purely imaginary, including zero.2. The cross elements of a skew-Hermitian matrix are complex numbers having equal imaginary part values, and equal-in-magnitude-but-opposite-in-sign real parts.
Involtary Matrix A square matrix A such that A2=I or (A+I)(A-I)=0, A is called involtary matrix.
The null matrix is also called the zero matrix. It is a matrix with 0 in all its entries.
can anyone give me an exact definition of payroll matrix................
Well the one definition of asymmetric is: anything that fails to be symmetric.So a possible sentence if your working with math could be:The equation is clearly asymmetric.
Zero Matrix When all elements of a matrix are zero than the matrix is called zero matrix. Example: A=|0 0 0|
Identity or Unit Matrix If in the scaler matrix the value of k=1, the matrix is called the identity or unit matrix. It is denoted by I or U.
Lower-triangular Matrix A square matrix A whose elements aij=0 for i
Diagonal Matrix A square matrix A which is both uper-triangular and lower triangular is called a diagonal matrix. Diagonal matrix is denoted by D.
A square matrix A is idempotent if A^2 = A. It's really simple
Scaler Matrix If in the diagonal matrix D, a11=a22=a33=...=ann=k. Then D is called a scaler matrix.
from data structure
Uper-triangular Matrix A square matrix A whose elements aij=0 for i>j is called upper triangular matrix.