Examples of 'orthogonal matrix' in a sentence
Meaning of "orthogonal matrix"
An orthogonal matrix is a square matrix in which rows and columns are orthonormal vectors, meaning the dot product of each pair of distinct vectors is zero, and the length of each vector is 1. These matrices play a crucial role in various mathematical operations and transformations
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- A square matrix whose columns, considered as vectors, are orthonormal to each other. This implies that the transpose of such a matrix is also its inverse.
How to use "orthogonal matrix" in a sentence
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orthogonal matrix
The inverse of an orthogonal matrix is its transpose.
Note that a real symmetric matrix is diagonalizable by an orthogonal matrix.
The complex analogue of an orthogonal matrix is a unitary matrix.
An orthogonal matrix is a matrix whose column vectors form an orthonormal set.
Consequently every orthogonal matrix is invertible.
Let us recall that any real symmetric matrix may be diagonalized by an orthogonal matrix.
Therefore a precise orthogonal matrix is excluded.
The Clebsch-Gordan coefficients form a real orthogonal matrix.
The transpose of the orthogonal matrix is also orthogonal.
Preferably, the coding matrix is a real orthogonal matrix.
An arbitrary orthogonal matrix which is not normalized may be used.
The rotation matrix is an orthogonal matrix.
Real orthogonal matrix.
Is diagonalizable by an orthogonal matrix.
Any orthogonal matrix of size n × n can be constructed as a product of at most n such reflections.
See also
orthogonal frequency division multiplexing
orthogonal group
orthogonal polynomials
orthogonal projection
orthogonal group
orthogonal polynomials
orthogonal projection
Where is an orthogonal matrix.
An orthogonal matrix is the real specialization of a unitary matrix, and thus always a normal matrix.
Keep in mind that the inverse of an orthogonal matrix is the matrix transpose.
Transmission method according to claim 2, wherein the real coding matrix is a real orthogonal matrix.
Then there exists an orthogonal matrix and a diagonal matrix such that.
As a result, the transpose of Q is equal to the inverse of Q, Q is an orthogonal matrix.
If A is an orthogonal matrix then.
In this case, because and are real valued, they each are an orthogonal matrix.
Then, there is an orthogonal matrix such that.
In this case, because U and V ∗ are real valued, each is an orthogonal matrix.
Then, there is a real orthogonal matrix such that.
Every orthogonal matrix has determinant 1 or -1.
This problem is equivalent to finding the nearest orthogonal matrix to a given matrix.
The determinant of an orthogonal matrix is equal to 1 or -1.
Thus every rotation can be represented uniquely by an orthogonal matrix with unit determinant.
The determinant of an orthogonal matrix is always 1 or -1.
The product of two such matrices is a special orthogonal matrix that represents a rotation.
Alternatively, we can determine a best orthogonal matrix to find the rotation parameters r1, r2, r3.
In other words P is an orthogonal matrix.
As a linear transformation, every special orthogonal matrix acts as a rotation.
An indirect isometry is an affine transformation with an orthogonal matrix that has a determinant of -1.
Here, a method for selecting the Nth normal orthogonal matrix will be concretely explained.
Show that the determinant of an orthogonal matrix is either 1 or -1.
Thus, the determinant of a rotation orthogonal matrix must be 1.
That is, P is an orthogonal matrix.
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Avoid orthogonal walls corners of room in particular
Anything in v perp perp is orthogonal to anything in v perp
The orthogonal components are now readily identified
Examples of using Matrix
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Mass of each version a matrix shall be provided
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