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相关概念视频

Scalar and Vector Triple Products01:06

Scalar and Vector Triple Products

2.3K
Two vectors can be multiplied using a scalar product or a vector product. The resultant of a scalar product is scalar, while with vector products, the resultant is a vector. These rules of the scalar or vector product between two vectors can be applied to multiple vectors to obtain meaningful combinations. The scalar triple product is the dot product of a vector with the cross product of two vectors.
The scalar triple product is the dot product of a vector with the cross product of two vectors....
2.3K
Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

13.4K
It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...
13.4K
Vector Representation of Complex Numbers01:16

Vector Representation of Complex Numbers

94
Complex numbers, represented in Cartesian coordinates, can also be visualized as vectors. These vectors can be expressed in polar form, emphasizing their magnitude and angle. When a complex number is input into a function, the output is another complex number, highlighting the function's zero point from which the vector representation can originate.
Consider a function defined as the product of the complex factors in the numerator divided by the product of the complex factors in the...
94
Scalar Product (Dot Product)01:11

Scalar Product (Dot Product)

8.1K
The scalar multiplication of two vectors is known as the scalar or dot product. As the name indicates, the scalar product of two vectors results in a number, that is, a scalar quantity. Scalar products are used to define work and energy relations. For example, the work that a force (a vector) performs on an object while causing its displacement (a vector) is defined as a scalar product of the force vector with the displacement vector.
The scalar product of two vectors is obtained by multiplying...
8.1K
Couples: Scalar and Vector Formulation01:21

Couples: Scalar and Vector Formulation

211
One might wonder how the captain of a large ship can navigate through the ocean with just a turn of the steering wheel. The answer lies in the concept of two parallel forces that are equal in magnitude and opposite sense, creating a couple moment.
A couple moment is a rotational force that tends to rotate the steering wheel. The wheel's rotation can either be in a clockwise or anticlockwise direction. The right-hand rule is a helpful method for determining the direction of a couple moment....
211
Vector Operations01:20

Vector Operations

1.1K
Vectors are physical quantities that have both magnitude and direction. The vector operations include addition, subtraction, and scalar multiplication.
A vector multiplied by a scalar value is called scalar multiplication. The result obtained is a new vector with a different magnitude. If the scalar is positive, the direction of the vector remains the same, but if it is negative, the direction of the vector is reversed. For example, the product of the mass and velocity yields the momentum.
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相关实验视频

Updated: May 16, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

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复杂值矩阵向量乘法使用可扩展的连贯光子处理器.

Yiwei Xie1, Xiyuan Ke1, Shihan Hong1

  • 1State Key Laboratory of Extreme Photonics and Instrumentation, Zhejiang Key Laboratory of Optoelectronic Information Technology, College of Optical Science and Engineering, Zhejiang University, Hangzhou 310058, China.

Science advances
|April 4, 2025
PubMed
概括
此摘要是机器生成的。

我们开发了一个16通道的光子处理器,用于超快的矩阵向量乘法 (MVM). 这种芯片规模的设备每秒实现1.28太运算,为人工智能和信号处理推进光子计算.

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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
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Multimodal Volumetric Retinal Imaging by Oblique Scanning Laser Ophthalmoscopy oSLO and Optical Coherence Tomography OCT
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相关实验视频

Last Updated: May 16, 2025

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Generation and Coherent Control of Pulsed Quantum Frequency Combs

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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

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Multimodal Volumetric Retinal Imaging by Oblique Scanning Laser Ophthalmoscopy oSLO and Optical Coherence Tomography OCT
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科学领域:

  • 光子学 是一个光子学.
  • 光学计算是指光学计算的应用.
  • 人工智能的人工智能

背景情况:

  • 矩阵向量乘法 (MVM) 对于信号处理和AI至关重要.
  • 光子处理器提供了比电子对应器更高的速度和能源效率的潜力.
  • 现有的光子解决方案面临着可扩展性和灵活性方面的挑战.

研究的目的:

  • 提出和演示一种新的芯片规模连贯光子矩阵向量乘法处理器 (MVMP).
  • 为了实现高级应用程序的高速计算和功能灵活性.
  • 克服当前微电子和光子计算方法的局限性.

主要方法:

  • 集成一个可编程的16通道芯片上的相干光子处理器.
  • 使用低相误差的马赫-泽恩德干扰仪网格.
  • 采用超低损耗扩展光子波导延迟线用于振幅和相位编码.
  • 高速连贯检测的实施.

主要成果:

  • 复杂值矩阵向量乘法以每秒1.28特拉运算 (TOPS) 的演示.
  • 实现了对任意矩阵转换,并行图像处理和手写数字识别的高度灵活性.
  • 验证了低损耗和低相误差设计的优点,以提高可扩展性和功能灵活性.

结论:

  • 拟议的MVMP代表了高速和大规模光子计算的重大进步.
  • 综合设计能够显著提高计算速度和能源效率.
  • 这项技术对未来的人工智能和信号处理应用具有前景.