If a matrix is said to be orthogonal, what property does it have?
Practice Questions
Q1
If a matrix is said to be orthogonal, what property does it have?
All elements are zero
Transpose is equal to its inverse
All diagonal elements are equal
It is a square matrix
Questions & Step-by-Step Solutions
If a matrix is said to be orthogonal, what property does it have?
Step 1: Understand what a matrix is. A matrix is a rectangular array of numbers arranged in rows and columns.
Step 2: Know what a square matrix is. A square matrix has the same number of rows and columns.
Step 3: Learn about the transpose of a matrix. The transpose of a matrix is formed by flipping it over its diagonal, switching the row and column indices.
Step 4: Understand what an inverse of a matrix is. The inverse of a matrix is another matrix that, when multiplied with the original matrix, gives the identity matrix.
Step 5: Define an orthogonal matrix. An orthogonal matrix is a square matrix where the transpose of the matrix is equal to its inverse.
Step 6: Recognize the property of orthogonal matrices. This means that if you take the transpose of the orthogonal matrix and multiply it by the original matrix, you will get the identity matrix.
Orthogonal Matrix – An orthogonal matrix is a square matrix whose rows and columns are orthonormal vectors, meaning that the transpose of the matrix is equal to its inverse.
