# Which of the following is a diagonal matrix

## What is diagonal matrix example?

**Identity matrix, null matrix, and scalar matrix**are examples of a diagonal matrix as each of them has its non-principal diagonal elements to be zeros. The sum of two diagonal matrices is a diagonal matrix.

## What is a diagonal matrix?

In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices. Elements of the main diagonal can either be zero or nonzero.

## How do you find diagonal matrix?

**We want to diagonalize the matrix if possible.**

- Step 1: Find the characteristic polynomial. …
- Step 2: Find the eigenvalues. …
- Step 3: Find the eigenspaces. …
- Step 4: Determine linearly independent eigenvectors. …
- Step 5: Define the invertible matrix S. …
- Step 6: Define the diagonal matrix D. …
- Step 7: Finish the diagonalization.

## Is zero matrix is diagonal matrix?

**also diagonal**. Provided it is a square matrix. An upper triangular matrix is one in which all entries below the main diagonal are zero.

## Is 1 a diagonal matrix?

Yes, every 1×1 matrix is diagonal.

## What is a diagonal and example?

The definition of diagonal is something with slanted lines or a line that connects one corner with the corner furthest away. An example of diagonal is a line going from the bottom left corner of a square to the top right corner. … (geometry) A line joining non-adjacent vertices of a polygon.

## Is diagonal matrix triangular matrix?

**both upper and lower triangular since**they have zeroes above and below the main diagonal. The inverse of a lower triangular matrix is also lower triangular. The product of two or more lower triangular matrices is also lower triangular.

## What is right diagonal matrix?

**The sum of the row and column indexes of a right diagonal element is always one less than the size (order) of the matrix**i.e. i+j==size-1.

## What are diagonal in math?

**a line segment joining two vertices of a polygon or polyhedron**, when those vertices are not on the same edge. … In matrix algebra, a diagonal of a square matrix is a set of entries extending from one corner to the farthest corner. There are also other, non-mathematical uses.

## What is an orthogonal matrix example?

**its transpose is equal to the inverse matrix of it**. In other words, the product of a square orthogonal matrix and its transpose will always give an identity matrix.

## What is skew symmetric matrix with example?

**A transposed form of a matrix that is equal to the negative of that matrix**is called a skew-symmetric matrix. This is an example of a skew-symmetric matrix: B=[02−20] B = [ 0 2 − 2 0 ]

## How do you find a triangular matrix?

## Are diagonal matrices orthogonal?

**Every diagonal matrix is orthogonal**. … If A is an n×n orthogonal matrix, and x and y are any non-zero column vectors in Rn, then the angle between x and y is equal to the angle between Ax and Ay.

## Which of the following is orthogonal matrix?

**square matrix A**is said to be orthogonal if ATA=I If A is a sqaure matrix of order n and k is a scalar, then |kA|=Kn|A|Also|AT|=|A| and for any two square matrix A d B of same order AB|=|A∣|B| On the basis of abov einformation answer the following question: If A is an orthogonal matrix then (A) AT is an orthogonal …

## Is a skew symmetric matrix?

**if and only if it is the opposite of its transpose**. All main diagonal entries of a skew-symmetric matrix are zero.

## Is diagonal matrix a square matrix?

**a square matrix in which all off-diagonal entries are zero**. (Note that a diagonal matrix is necessarily symmetric.)

## Are all diagonal matrices invertible?

**Most matrices are invertible**: Since the determinant is a polynomial in the matrix entries, the set of matrices with determinant equal to is a subvariety of dimension .

## How many diagonals does a matrix have?

**two**, but only one is important – the diagonal stretching from top left to bottom right. How many diagonals are in a 3×3 matrix? The diagonal of a square matrix is usually from the top left to the bottom right.

## What is diagonal shape?

**a straight line joining two nonadjacent vertices of a shape**, that is, two corners of a shape that are not next to each other. … For example, a kite has two angles which are the same size, and these angles are diagonally opposite each other.

## What is invertible diagonal matrix?

**if an only if its kernel is 0**, and an element of the kernel is the same thing as an eigenvector with eigenvalue 0, since it is mapped to 0 times itself, which is 0. … So if P−1AP is diagonal, then P−1AP is invertible if an only if none of its diagonal entries (eigenvalues) are 0.

## Why are diagonal matrices invertible?

**invertible if and only if its eigenvalues are nonzero**.

## Is the inverse of a diagonal matrix a diagonal matrix?

**diagonal matrix**where the elements of the main diagonal are the reciprocals of the corresponding elements of the original diagonal matrix.

## What is the transpose of a diagonal matrix?

Property 1: If addition or multiplication is being applied on diagonal matrices, then the matrices should be of the same order. … Property 2: When you transpose a diagonal matrix, **it is just the same as the original because all the diagonal numbers are 0**.