Orthogonal Matrix Calculator Online

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Orthogonal Matrix Calculator Description

Explanation:

When the matrix's transpose equals its inverse, the matrix is said to be orthogonal. Let's review what a matrix's transpose is. The resulting matrix is known as the transposed matrix if we choose to write a matrix's rows as columns (or) its columns as rows. We already know about that a matrix is considered symmetric if its transpose equals its original matrix. An orthogonal matrix, however, is one in which the transpose of the matrix equals the inverse of the original matrix.

What is An Orthogonal Matrix?

A square matrix is an orthogonal matrix if and only if its transpose is the same as its inverse. In other words,
AT = A-1, where AT is actually the transpose of A and inverse of A is A-1.
A square matrix for example 'A' is said to be "orthogonal" if

  • AAT = ATA = I (or)
  • AT = A-1

    • Properties of Normal Matrix

    An orthogonal matrix (A) characteristics's are listed below depending on its definition.

    • In orthogonal matrix, the Inverse and Transpose are equivalent. i.e., AT = A-1.
    • The transpose of A and it product is an identity matrix calculated in any order. i.e., AAT = ATA = I
    • The determinant of orthogonal matrix is always be 1 or -1 which means the orthogonal matrix is always be a non-singular matrix because its determinant is not equal to zero.
    • A diagonal matrix whose elements or entries are either 1 or -1 is always orthogonal.
    • As AT = A-1, So AT and AT both are orthogonal.
    • The eigenvalues of matrix A are +1 or -1 and the eigenvectors are also orthogonal.
    • As I · I = I · I = I, So the identity matrix is orthogonal.

    How to use check Orthogonal Matrix Calculator?

    • Firstly, you need to enter the dimension of the matrix. Enter number of rows in "Rows" input field and Enter number of columns in "Columns" input field.
    • Then press the button "Set Matrix".
    • An empty matrix will appear below and then you can enter your values inside the matrix.
    • After entering all the values press "Solve" button, the result will automatically appear below which check whether the matrix is Orthogonal matrix or not.

    Orthogonal Matrix Example Image:

    Orthogonal Matrix example

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    Keywords

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    • What are Orthogonal Matrices?
    • How to Know if a Matrix is Orthogonal?
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