Sum of diagonal elements of a square matrix is known as
Answers
Answer:
In mathematics, a square matrix is a matrix with the same number of rows and columns. An n-by-n matrix is known as a square matrix of order n. Any two square matrices of the same order can be added and multiplied.
Square matrices are often used to represent simple linear transformations, such as shearing or rotation. For example, if R is a square matrix representing a rotation (rotation matrix) and v is a column vector describing the position of a point in space, the product Rv yields another column vector describing the position of that point after that rotation. If v is a row vector, the same transformation can be obtained using vRT, where RT is the transpose of R.
Answer:
The sum of the diagonal elements of a square matrix is referred to as the trace of the matrix.
Step-by-step explanation:
- The trace of a square matrix A, called tr(A), is defined as the sum of elements on A's principal diagonal (from upper left to lower right) in linear algebra.
- A square matrix (n×n) is the only matrix for which the trace is specified.
- It may be demonstrated that a matrix's trace is equal to the sum of its (complex) eigenvalues (counted with multiplicities).