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Asymptotically orthogonal hashing functions refer to a class of hash functions designed to minimize collisions, meaning that the probability of two different inputs producing the same hash output approaches zero as the input size increases. This property is crucial for applications in cryptography and data structures, where the uniqueness of hash outputs is essential for efficiency and security. The term "asymptotically" indicates that this behavior improves with larger input sizes, making these functions particularly effective in handling large datasets.
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What does the mean of product of two orthogonal matrix is orthogonal in terms of rotation?
The mean of the product of two orthogonal matrices, which represent rotations, is itself an orthogonal matrix. This is because the product of two orthogonal matrices is orthogonal, preserving the property that the rows (or columns) remain orthonormal. When averaging these rotations, the resulting matrix maintains orthogonality, indicating that the averaged transformation still represents a valid rotation in the same vector space. Thus, the mean of the rotations captures a new rotation that is also orthogonal.
What is a vector which is orthogonal to the other vectors and is coplanar with the other vectors called?
In a plane, each vector has only one orthogonal vector (well, two, if you count the negative of one of them). Are you sure you don't mean the normal vector which is orthogonal but outside the plane (in fact, orthogonal to the plane itself)?
What does orthogonal mean in mathematics?
At right angles - in two or more dimensions.
Prove that the product of two orthogonal matrices is orthogonal and so is the inverse of an orthogonal matrix What does this mean in terms of rotations?
To prove that the product of two orthogonal matrices ( A ) and ( B ) is orthogonal, we can show that ( (AB)^T(AB) = B^TA^TA = B^T I B = I ), which confirms that ( AB ) is orthogonal. Similarly, the inverse of an orthogonal matrix ( A ) is ( A^{-1} = A^T ), and thus ( (A^{-1})^T A^{-1} = AA^T = I ), proving that ( A^{-1} ) is also orthogonal. In terms of rotations, this means that the combination of two rotations (represented by orthogonal matrices) results in another rotation, and that rotating back (inverting) maintains orthogonality, preserving the geometric properties of rotations in space.
What are the two squiggly lines together mean in math?
In mathematics, two squiggly lines together (∼∼) typically indicate a relation of equivalence or similarity between two objects. For instance, in set theory, it can denote that two sets are equivalent in size (they have the same cardinality). In other contexts, it may represent that two functions or sequences are asymptotically equivalent. The specific meaning often depends on the context in which it is used.
What does the mean of product of two orthogonal matrix is orthogonal in terms of rotation?
The mean of the product of two orthogonal matrices, which represent rotations, is itself an orthogonal matrix. This is because the product of two orthogonal matrices is orthogonal, preserving the property that the rows (or columns) remain orthonormal. When averaging these rotations, the resulting matrix maintains orthogonality, indicating that the averaged transformation still represents a valid rotation in the same vector space. Thus, the mean of the rotations captures a new rotation that is also orthogonal.
What is a vector which is orthogonal to the other vectors and is coplanar with the other vectors called?
In a plane, each vector has only one orthogonal vector (well, two, if you count the negative of one of them). Are you sure you don't mean the normal vector which is orthogonal but outside the plane (in fact, orthogonal to the plane itself)?
What does orthogonal mean in mathematics?
At right angles - in two or more dimensions.
Prove that the product of two orthogonal matrices is orthogonal and so is the inverse of an orthogonal matrix What does this mean in terms of rotations?
To prove that the product of two orthogonal matrices ( A ) and ( B ) is orthogonal, we can show that ( (AB)^T(AB) = B^TA^TA = B^T I B = I ), which confirms that ( AB ) is orthogonal. Similarly, the inverse of an orthogonal matrix ( A ) is ( A^{-1} = A^T ), and thus ( (A^{-1})^T A^{-1} = AA^T = I ), proving that ( A^{-1} ) is also orthogonal. In terms of rotations, this means that the combination of two rotations (represented by orthogonal matrices) results in another rotation, and that rotating back (inverting) maintains orthogonality, preserving the geometric properties of rotations in space.
What does the word hashing mean in Tillie Olsen's I Stand Here Ironing?
In "I Stand Here Ironing," hashing refers to the protagonist's method of ironing with smooth, circular movements. The act of hashing represents the mother's attempt to find a sense of order and control in her life as she reflects on her past decisions and struggles with guilt and regret.
What is mean by orthogonal frequency code division multiplexing in wireless communication?
Orthogonal frequency division multiplexing is special case of frequency division multiplexing where a ling serial data streams are divided into parallel data streams and each data stream is multiplied either by orthogonal frequency or code. when multiplied by code known as frequency code division multiplexing and when multiplied by orthogonal frequency then know as orthogonal frequency division multiplexing
What does the quote you eat in dreams the custard of the day mean?
It implies that your dreams are just a re-hashing of your experiences during your waking life.
What does hashing mean and how is it used in computer science and cryptography?
Hashing is a process in computer science and cryptography where data is converted into a fixed-size string of characters, known as a hash value. This hash value is unique to the input data and is used for various purposes such as data retrieval, data integrity verification, and password storage. In cryptography, hashing is used to securely store passwords and verify data integrity by comparing hash values.
What is mean by PasswordUtils?
PasswordUtils is a fast, simple and lightweight utility class containing series of methods for creating, comparing, hashing, and random generating secure passwords to be stored on database or used for other purposes. It uses Java's latest built-in hashing algorithms and is independent of any other libraries.
What are the two squiggly lines together mean in math?
In mathematics, two squiggly lines together (∼∼) typically indicate a relation of equivalence or similarity between two objects. For instance, in set theory, it can denote that two sets are equivalent in size (they have the same cardinality). In other contexts, it may represent that two functions or sequences are asymptotically equivalent. The specific meaning often depends on the context in which it is used.
What does it mean when the dot product between two vectors is zero?
When the dot product between two vectors is zero, it means that the vectors are perpendicular or orthogonal to each other.
What does 'general properties' mean?
its functions
