Arithmetic Sequence Examples with nth term and Common Difference

A sequence is a fundamental arrangement of things, objects, numbers, etc. The sequences may be finite or infinite depending on the number of terms. There are many types of sequences such as geometric sequence, harmonic sequence, and arithmetic sequence which are used to perform the requisite operation. In this topic, we only discuss the arithmetic … Read more

Cayley-Hamilton Theorem

Cayley-Hamilton theorem states that every square matrix satisfies its own characteristic equation. This theorem is named after two mathematicians, Arthur Cayley & William Rowan Hamilton. This theorem provides an alternative way to find the inverse of a matrix. Let aoλn + a1λn-1 + a2λn-2 + ………………. + an-2λ2 + an-1λ + an = 0 be … Read more

Determinant Properties

The determinant of matrix P is denoted as |P| i.e. matrix name between two parallel lines. It is also written as det(P) or by symbol delta (Δ). The determinant is always calculated for a square matrix. So if we talk about matrix in this article then it will be understood as a square matrix. In … Read more

Conjugate of a Matrix – Example and Properties

Conjugate of a matrix is the matrix obtained from matrix ‘P’ on replacing its elements with the corresponding conjugate complex numbers. It is denoted by $\overline{P}$. Conjugate of a matrix example Let Q is a matrix such that \[Q=\begin{bmatrix} 1+i &2+3i \\ 4-2i& 6 \end{bmatrix}\] Now, to find the conjugate of this matrix Q, we … Read more

Conjugate Transpose of a Matrix – Example and Properties

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

What is Unitary Matrix? Example

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