Write down the properties of orthogonal matrix.
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The orthogonal matrix possesses the following properties:
1) Every identity matrix is an orthogonal matrix.
2) The diagonal matrix is an orthogonal one.
3) Let P be an orthogonal matrix of order n. Also, "a" and "b" be any two column vectors in Rn, then
i) (Pa) . (Pb) = ab
ii) (Pa)T . (Pb) = aTb
4) When a collection of n × n orthogonal matrices is gathered in the form of a group, it is called an orthogonal group and is denoted by On.
5) If A be an orthogonal matrix, then its transpose i.e. AT will also be an orthogonal matrix.
6) Similarly, inverse of an orthogonal matrix i.e. A−1 is also an orthogonal matrix.
7) The product of an orthogonal matrix and its transpose matrix is equal to the identity matrix of same order.
8) The value of determinant of orthogonal matrix is "±1".
9) The eigenvalues of an orthogonal matrix are ±1. Also, the its eigenvectors would also be orthogonal and real.
10) In an orthogonal matrix, the vector inner product of any two row vectors or any two column vectors is equal to zero.
11) An orthogonal matrix is always a symmetric matrix.
12) The product of two orthogonal matrices is also orthogonal.
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The orthogonal matrix possesses the following properties:
1) Every identity matrix is an orthogonal matrix.
2) The diagonal matrix is an orthogonal one.
3) Let P be an orthogonal matrix of order n. Also, "a" and "b" be any two column vectors in Rn, then
i) (Pa) . (Pb) = ab
ii) (Pa)T . (Pb) = aTb
4) When a collection of n × n orthogonal matrices is gathered in the form of a group, it is called an orthogonal group and is denoted by On.
5) If A be an orthogonal matrix, then its transpose i.e. AT will also be an orthogonal matrix.
6) Similarly, inverse of an orthogonal matrix i.e. A−1 is also an orthogonal matrix.
7) The product of an orthogonal matrix and its transpose matrix is equal to the identity matrix of same order.
8) The value of determinant of orthogonal matrix is "±1".
9) The eigenvalues of an orthogonal matrix are ±1. Also, the its eigenvectors would also be orthogonal and real.
10) In an orthogonal matrix, the vector inner product of any two row vectors or any two column vectors is equal to zero.
11) An orthogonal matrix is always a symmetric matrix.
12) The product of two orthogonal matrices is also orthogonal.
hope it helped you....
pls mark me as the brainliest....
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