Conjugate transpose of a matrix ‘P’ is basically a matrix which is equal to the conjugate of the matrix obtained by taking the transpose of the matrix ‘P’. In order to find the conjugate transpose of any matrix; firstly, transpose is obtained and secondly, the conjugate is obtained. The conjugate transpose is generally denoted as … Read more
When the conjugate transpose of a complex square matrix is equal to the inverse of itself, then such matrix is called as unitary matrix. If Q is a complex square matrix and if it satisfies Qθ = Q-1 then such matrix is termed as unitary. Please note that Qθ and Q-1 represent the conjugate transpose and inverse of the matrix Q, … Read more
When the conjugate transpose of a complex square matrix is equal to the negative of itself, then this matrix is called as skew hermitian matrix. If P is a complex square matrix and if it satisfies Pθ = -P then such matrix is termed as skew hermitian. It is noted that Pθ represents the conjugate transpose of matrix P. … Read more
When the conjugate transpose of a complex square matrix is equal to itself, then such matrix is known as hermitian matrix. If B is a complex square matrix and if it satisfies Bθ = B then such matrix is termed as hermitian. Here Bθ represents the conjugate transpose of matrix B. The conjugate transpose of a matrix … Read more
Orthogonal matrix is a square matrix R=[xij] such that RT = R-1. In other words, a square matrix (R) whose transpose is equal to its inverse is known as orthogonal matrix i.e. RT = R-1. Orthogonal matrix examples The best example of an orthogonal matrix is an identity matrix or unit matrix as shown below. \[I=\begin{bmatrix} 1 &0 … Read more
Skew symmetric matrix is a square matrix Q=[xij] in which (i, j)th element is negative of the (j, i)th element i.e. xij = -xji for all values of i and j. In other words, a square matrix (Q) which is equal to negative of its transpose is known as skew-symmetric matrix i.e. QT = -Q. Skew symmetric matrix examples The example … Read more
Symmetric matrix is a square matrix P=[xij] in which (i, j)th element is similar to the (j, i)th element i.e. xij = xji for all values of i and j. In other words, a square matrix (P) which is equal to its transpose is known as symmetric matrix i.e. PT = P. Symmetric matrix examples The … Read more
Air conditioning systems have standard electrical parts that are essential for temperature control, equipment protection and minimizing equipment operation costs. These electric parts vary from wiring to sophisticated control system circuitry. Electrical Components of Air Conditioning System Capacitor The capacitor absorbs and stores electricity from the main supply. Capacitors maintain a constant supply of charge … Read more
You definitely want your car to look like it was bought yesterday out of the showroom. But it will not look like that every day. With time the look of your car will fade. But definitely, there are ways to keep your car clean and new. These are more like applying a new coat of … Read more
Singular matrix is a square matrix whose determinant is zero. It is also known as non invertible matrix or degenerate matrix. A square matrix whose determinant is not zero is known as non singular matrix. It is also known as invertible matrix or non degenerate matrix. A square matrix P is said to be singular matrix … Read more