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The Definition of an Anti-Symmetric Matrix:
If a square matrix, A, is equal to its negative transpose, -A', then A is an anti-symmetric matrix.
Notes:
1. All diagonal elements of A must be zero.
2. The cross elements of A must have the same magnitude, but opposite sign.
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What is the definition of an idempotent matrix?
A square matrix A is idempotent if A^2 = A. It's really simple
Is the row space of matrix an equivalent to the column space of matrix AT which is the transpose of matrix A?
Since the columns of AT equal the rows of A by definition, they also span the same space, so yes, they are equivalent.
What is the definition of a Hermitian matrix?
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.
What is an orthogonal matrix?
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.
What is the definition of a skew-Hermitian matrix?
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.
What is the definition of involtary matrix?
Involtary Matrix A square matrix A such that A2=I or (A+I)(A-I)=0, A is called involtary matrix.
What is the definition of a null matrix?
The null matrix is also called the zero matrix. It is a matrix with 0 in all its entries.
What is payroll matrix?
can anyone give me an exact definition of payroll matrix................
What is a sentence for antisymmetric?
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.
What is the definition of zero matrix?
Zero Matrix When all elements of a matrix are zero than the matrix is called zero matrix. Example: A=|0 0 0|
What is the definition of identity matrix?
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.
Definition of Lower-triangular matrix?
Lower-triangular Matrix A square matrix A whose elements aij=0 for i
What is the definition of a diagonal matrix?
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.
What is the definition of an idempotent matrix?
A square matrix A is idempotent if A^2 = A. It's really simple
What is the definition of scaler matrix?
Scaler Matrix If in the diagonal matrix D, a11=a22=a33=...=ann=k. Then D is called a scaler matrix.
Definition of dope matrix?
from data structure
What is the definition of Uper-triangular matrix?
Uper-triangular Matrix A square matrix A whose elements aij=0 for i>j is called upper triangular matrix.
