# 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 scaler matrix?

Scaler Matrix If in the diagonal matrix D, a11=a22=a33=...=ann=k. Then D is called a scaler matrix.

### What is the definition of a symmetric matrix?

Symmetric Matrix: Given a square matrix A such that A'=A, where A' is the transpose of A, then A is a symmetric matrix. note: No need to think about diagonal elements, they can be anything.

### Is the scalar matrix is always a identity matrix?

No. A scalar matrix is a diagonal matrix whose main diagonal elements are the same. Only if the diagonal elements are all 1 is it an identity matrix.

### What is the definition of an anti-symmetric matrix?

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.

### Is a matrix multiplied by its transpose diagonalisable?

It will be a square matrix and, to that extent, it is diagonalisable. However, the diagonal elements need not be non-zero. It will be a square matrix and, to that extent, it is diagonalisable. However, the diagonal elements need not be non-zero. It will be a square matrix and, to that extent, it is diagonalisable. However, the diagonal elements need not be non-zero. It will be a square matrix and, to that extent, it is… Read More

### What is a minor diagonal matrix?

A minor diagonal matrix is one where the only non-zero entries are along the diagonal that runs from bottom most left to upper most right.

### 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 the determinant of a 3x3 diagonal matrix?

It is the product of the three diagonal elements.

### How do you Write A program in c language for checking a diagonal matrix?

Write a program in c++ that take input in a integer matrix of size 4*4 and find out if the entered matrix is diagonal or not.

### What is the trace of a matrix to a power?

It is the diagonal entries of the matrix raised to a power.

### What is strictly lower triangular matrix?

A strictly lower triangular matrix is a kind of (lower) triangular matrix. Term "lower" implies matrix has elements only in the lower half. The condition "strictly" implies that even the "diagonal" of such lower triangular matrix is populated with '0's. The strictly lower triangular matrix thus has '0's in its diagonal as well as the upper triangle part. In other words, a strictly lower triangular matrix is a lower triangular matrix minus its diagonal.

### Wap to build a sparse matrix as an arraywrite functions to check if the sparse matrix is a square diagonal or lower triangular or upper triagular or tridiagonal matrix?

write a programe to build a sparse matrix as an array. write function to check if the sparse matrix is a square, diagonal,lower triangular, upper triangular or tridiagonal matrix

### What does it mean for a matrix to be triangular?

A square matrix in which all the entries of the main diagonal are zero

### Example of commutative matrix?

The identity matrix, which is a square matrix with zeros everywhere except on the principal diagonal where they are all ones.

### What is a unit matrix?

It is a square matrix whose main diagonal has only 1's and all other positions in the matrix are 0.

### 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 a mathematical kite?

a quadrilateral in which diagonal are not congruent and larger diagonal is perpendicular bisector of smaller diagonal then it is known as kite

### 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 significance of diagonal terms of variance-covariance matrix?

The diagonal terms give the variances. The square root of which gives the standard deviations. The diagonal terms give the variances. The square root of which gives the standard deviations.

### What is the definition of a kite how a kite works?

a quadrilateral in which diagonal are not congruent and larger diagonal is perpendicular bisector of smaller diagonal then it is known as kite -- M.S. Vighe

### What is payroll matrix?

can anyone give me an exact definition of payroll matrix................

### C program to find the sum of all diagonal elements of a matrix?

To find the sum of the diagonals of a given matrix the following code fragment can be used (with suitable definitions and data initialisations): if (num_rows > num_cols) max = num_cols; else max = num_rows; sum = 0; for (i = 0; i < max; i++) sum += matrix[i][i]; printf("Sum of diagonal elements is %d\n", sum);

### 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.

### What is the meaning of inverse matrices?

If, for an n*n matrix, A, there exists a matrix B such that AB = I, where I is the n*n identity matrix, then the matrix B is said to be the inverse of A. In that case, BA = I (in general, with matrices, AB â‰ BA) I is an n*n matrix consisting of 1 on the principal diagonal and 0s elsewhere.

### What is meant by tridiagonal matrix?

A tridiagonal matrix is one in which the only non-zero elements are on the principal diagonal, and the two diagonals immediately next to it: one below and the other above.

### Write a Program to find sum of all elements above and below the main diagonal of a square matrix?

#include<iostream.h> #include<conio.h> void main() { int a=0,b=0,i,j,s,c[10][10]; //initialising matrix cout<<"Enter size of square of Matrix \n"; cin>>s; cout<<"Enter Values into Matrix of side(s) "<<s<<"\n"; for(i=0; i<s; i++) // Input Matrix { for(j=0; j<s; j++) { cin>>c[i][j]; } } cout<<"\nThe Given Matrix is\n"; // Output MAtrix for(i=0; i<s; i++) { cout<<"\n"; for(j=0; j<s; j++) { cout<<c[i][j]; } } cout<<"\n"; for(i=0; i<s; i++) // Loop to add elemnts below main diagonal { for(j=0; j<s; j++) if(i>j) a… Read More

### What is the definition of an idempotent matrix?

A square matrix A is idempotent if A^2 = A. It's really simple

### What is density matrix in quantum mechanics?

It is a Hermitian positive-semidefinite matrix of trace one that describes the statistical state of a quantum system. Hermitian matrix is defined as A=A^(dagger). Meaning that NxN matrix A is equal to it's transposed complex conjugate. Trace is defined as adding all the terms on the diagonal.

### 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.

### Definition of Lower-triangular matrix?

Lower-triangular Matrix A square matrix A whose elements aij=0 for i<j is called lower triangular matrix.

### What is the definition of unitary matrix?

It is the conjugate transpose of the matrix. Of course the conjugate parts only matters with complex entries. So here is a definition: A unitary matrix is a square matrix U whose entries are complex numbers and whose inverse is equal to its conjugate transpose U*. This means that U*U = UU* = I. Where I is the identity matrix.

### What is identity matrix?

It is a square matrix whose principal diagonal (top-left to bottom-right) are 1s and all other entries are 0. It has the property that if it is used to pre- or post-multiply any square matrix M (of the same size), then the result is M.

### Pgm to check given matrix is diagonal or not?

#include <stdio.h> #include <conio.h> void main() { int a[3][3],i,j,flg=0,flg2=0; clrscr(); printf("\n\t Enter 3*3 Matrix : "); for(i=0;i<3;i++) { for(j=0;j<3;j++) { scanf("%d",&a[i][j]); } } for(i=0;i<3;i++) { for(j=0;j<3;j++) { if(a[i]<a[j] && a[i][j]==0) { flg=flg+1; } if(a[i]>a[j] && a[i][j]==0) { flg2=flg2+1; } } } if(flg==3 && flg2==3) printf("\n\n Diagonal matrix !"); else printf("\n\n Not Diagonal matrix !"); getch(); }

### How do you enter only diagonal elements in c plus plus?

Matrices have two diagonals: main diagonal and anti-diagonal. The main diagonal runs from top-left to bottom-right. For square matrix A: // main diagonal: for (size_t xy=0; xy<A.size(); ++xy) cin >> A[xy][xy]; // anti-diagonal for (size_t x = A.size()-1, y=0; y<A.size(); --x; ++y cin >> A[x][y];

### What is a variance covariance matrix?

Briefly, the variance for a variable is a measure of the dispersion or spread of scores. Covariance indicates how two variables vary together. The variance-covariance matrix is a compact way to present data for your variables. The variance is presented on the diagonal (where the column and row intersect for the same variable), while the covariances reside above or below the diagonal.

### Definition of commutative matrix?

Commutative Matrix If A and B are the two square matrices such that AB=BA, then A and B are called commutative matrix or simple commute.

### What is the definition of transpose in regards to a matrix?

The Transpose of a Matrix The matrix of order n x m obtained by interchanging the rows and columns of the m X n matrix, A, is called the transpose of A and is denoted by A' or AT.

### What is the determinant of a 2x3 matrix?

The determinant function is only defined for an nxn (i.e. square) matrix. So by definition of the determinant it would not exist for a 2x3 matrix.

### How to find the Inverse of a square symmetric matrix?

You can factorize the matrix using LU or LDLT factorization algorithm. inverse of a diagonal matrix (D) is really simple. To find the inverse of L, which is a lower triangular matrix, you can find the answer in this link. www.mcs.csueastbay.edu/~malek/TeX/Triangle.pdf Since (A T )-1 = (A-1 )T for all matrix, you'll just have to find inverse of L and D.

### Definition of anti-commutative matrix?

Anti-Commutative Matrix If A and B are the two square matrices such that AB= - BA, then A and B are called anti-commutative matrix.

### How do you show that a square matrix A is similar to its transpose?

First we will handle the diagonalizable case. Assume A is diagonalizable, A=VDV-1. Thus AT=(V-1)TDVT, and D= VT AT(V-1)T. Finally we have that A= VVT AT(V-1)TV-1, hence A is similar to AT with matrix VVT. If A is not diagonalizable, then we must consider its Jordan canonical form, A=VJV-1, where J is block diagonal with Jordan blocks along the diagonal. Recall that a Jordan block of size m with eigenvalue at L is a mxm matrix… Read More

### Definition of nilpotent matrix?

Nilpotent Matrix A matrix A for which AP=0 where P is a positive integer is called nilpotent matrix. If P is the least positive integer for which AP=0 then A is said to be nilpotent of index P.

### What is this a line drawn between 2 vertices which are not next to each other?

This is a diagonal line. The definition of a diagonal is a line that joins two nonconsecutive vertices or corners of a polygon.

### What is the definition of diagonal in math?

A diagonal is a straight line joining any two non-adjacent vertices in a polygon or polyhedron or corresponding shapes in higher dimensional spaces.

### How many diagonals does a hexagon have one vertex?

None. By definition a diagonal goes from one vertex to another vertex and so each diagonal MUST have two vertices.