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Basic Mathematics of Artificial Intelligence

2026-02-23 17:28
2026-02-23 20:18

The mathematical foundation of artificial intelligence included many aspects: ** 1. Liner Algebra ** 1. ** Vectors and Matrices ** - Vectors were one-dimensional arrays that could represent direction and size, while matrices were two-dimensional arrays that could represent linear transformations. - For example, in artificial intelligence, linear algebra tools such as matrix multiplication were widely used in processing large data sets, image processing, and pattern recognition. 2. ** Transpose and Inverse Matrix ** - The transpose operation of the matrix is written as [A^{T}], and the inverse operation is written as [A^{-1}]. 3. ** System of linear equations ** - It could be solved by the Gauss elimination method. The determinate was a scalar-value of the matrix, which was used to determine whether the matrix was inverse. 4. ** Eigen Value and Eigen Vectors ** - The eigen values represent the scaling factor of the matrix in certain directions, and the eigen values correspond to the eigen values, representing the invariants of the matrix in certain directions. - Singular value decomposition (SVR) could decompose a matrix into the product of three matrices for dimensional reduction and data compression. ** 2. Theory of probability and statistics ** 1. ** Basic Concepts ** - The probability represents the probability of an event occurring, ranging from 0 to 1. - Condition probability (P(A| B) is the probability of an event occurring under a given condition. - Bayes 'theorem (P(A| B)=\frac{P(B| A)P(A)}{P(B)} is used to calculate the posteriori probability. 2. ** Random variables and distribution ** - The value of a scattered random variable is considered to be scattered, such as the binormal distribution or the poisson distribution, while the value of a continuous random variable is considered to be continuous, such as the normal distribution or the exponential distribution. - The expectation and the deviation represent the average and the degree of fluctuation of the random variable, respectively. - Maximum likelihood estimation (MLE) estimates the parameters by maximized the likelihood function, and Bayes estimation involves the prior distribution (the prior probability distribution of the parameters) and the posteriori distribution (the probability distribution of the parameters after observing the data). ** 3. Derivative ** 1. ** Limit and Derivative ** - The limit is the trend of the function around a certain point, the derivative is the instantaneous rate of change of the function at a certain point, recorded as <(x)> or <(dx)>, and the multi-variable function has a partial derivative <((x>)>. 2. ** Points ** - Indefinite integral was the process of finding the original function, and definite integral was the accumulation of the function in a certain interval. - The slope was the derivative of a multi-variable function, which represented the rate of change of the function in all directions. The slope descent method gradually adjusted the parameters through the slope direction to minimize the objective function. ** 4. Theory of optimization ** 1. ** Unconstrained optimization ** - The gradient-descent method minimized the objective function by gradually adjusting the parameters in the direction of the gradient-descent, and the Newton method used the second-order derivative (Hessian matrix) to accelerate convergence. 2. ** Restriction optimization ** - The Lagrange Multipliers Method transformed the constrained optimization problem into an unconstrained optimization problem by introducing the Lagrange Multipliers. - The Karush-Kuhn- Tucker (KMT) condition is used to solve optimization problems with unequal constraints. - The objective function and constraints in the concave optimization problem are both concave, and there is a global optimal solution. In addition, information theory was a mathematical theory that studied information transmission, storage, and processing, providing a theoretical basis for data compression and signal processing of artificial intelligence. Graph theory was used in search algorithms, decision trees, and other aspects to provide a basis for reasoning and decision-making of intelligent systems. The complexity theory evaluated the efficiency of artificial intelligence by analyzing the time complexity and space complexity of the algorithm. Group theory helped to understand and analyze complex data structures and patterns in image processing, pattern recognition, and encryption. There were also the applications of the Laplace transform, the Laplace transform, the random process, the numerical analysis, the subspace algebra, and so on in different fields of artificial intelligence such as image processing, speech recognition, and natural language processing. "A Short History of the Future: Legends of the Intelligent Era" was equally exciting. Everyone was welcome to click and read it!

Latest Questions

China porcelain English composition, Grade One, compulsory two

China has a long - standing history of porcelain production. Porcelain is one of the great inventions in China. It first emerged in ancient times and has since been continuously developed. Chinese porcelain is known for its high - quality raw materials. The clay used is carefully selected to ensure the fineness and purity of the porcelain. In terms of production techniques, Chinese porcelain - making is extremely sophisticated. From shaping the clay on the potter's wheel to the elaborate decoration process, every step requires the skills and experience of artisans. For example, the blue - and - white porcelain is famous for its beautiful blue patterns painted on white porcelain bodies. The styles of Chinese porcelain are diverse. There are simple and elegant types, as well as those with luxurious and complex decorations. These porcelain pieces not only have practical uses in daily life, such as for holding food and drinks, but also serve as important works of art. Chinese porcelain has had a profound impact on the world. It has been exported to many countries and regions, becoming a symbol of Chinese culture overseas. People all over the world are attracted by its beauty and elegance, which also promotes cultural exchanges between China and other countries. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>

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2026-08-25 05:57

The latest chapter in the novel of Lady Yunxiao's travel in another world

According to the information he had retrieved, he did not know the latest chapter of Lady Yunxiao's travel novel. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>

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2026-08-25 05:57

Which celebrities did the sixth princess interview?

The sixth princess had interviewed Wu Jinyan, Zhao Lusi, and other celebrities. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>

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2026-08-25 05:57

Top 10 Brands of Camping Table and Chairs

In 2023, the top 10 outdoor camping equipment brands (some of which included tables and chairs) were: Pathfinder/Toward, Moke/Ateurhike, Camel/Camel, Explorer, Decathlon/Decahlo, North Mountain Wolf, Tawa, Kaileshi/KAILAS1, Mugaodi/MOBIGARDE1, and Kawau/Kawau. In addition, among the top ten outdoor tables and chairs based on industry ratings, reputation, sales volume, and other 12 factors, the top ten brands were Waterman, Wei Camping, Mugao Di, Shangkaojia, Tokyo, Primitive, Explorer, Nuoke, Mondorfus, and Camel. The original work was equally exciting. You could click on the original work of "The Story of Rose" to understand the plot in advance!

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2026-08-25 05:56

There are many kinds of cultural relics, and they are very spectacular

Yes, the cultural relics were varied and spectacular. From China to other countries, a large number of cultural relics were produced in different regions, historical periods, and cultural backgrounds. In terms of types, cultural relics could be classified according to various methods such as era, existence form, region, texture, function, attribute, source, value, shape, etc. Interinternationally, they would also be divided into seven types from the perspectives of history, art, science, aesthetics, ethnography, and archeology: cultural relics, historical sites, architectural groups, heritage canals, heritage routes, historical towns and centers, and cultural landscapes. From the examples, there were many cultural relics such as the Tri-colored Glazed Tile of the Tang Dynasty, galloping horses, brick carvings, etc. in China, as well as exquisite artifacts such as the Autumn Cup of the Qing Dynasty, the Phoenix Crown of Empress Xiaoduan of the Ming Dynasty, and the hairpin of the Golden Cicada Jade Leaf of the Ming Dynasty. In foreign countries, there were cultural relics such as the marble carving of the Kiss of Death unearthed more than 3000 years ago and now hidden in the Sanxing Dui Museum, and the earliest human mirror made of obsidian excavated in Turkey more than 8,000 years ago. These cultural relics covered different materials, uses, artistic styles, and other aspects, showing the richness and richness of human civilization. Whether it was from the perspective of artistic value, historical value, or cultural value, they were all amazing. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>

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2026-08-25 05:56

Jade ware selling shop

There were many types of jade stores. For example, Wada City's Yuyan Jade Store was established on April 7th, 2022. It was located in Hotan Prefecture, Xinjiang, but it was currently in a state of deregistration. There was also Li Ming Jade Shop in Pingjiang District, Suzhou City. It was located in Suzhou, Jiangsu Province, and specialized in jade carving. In addition, the National Jade League Shiyu was a regular old shop that could be chosen when traveling in Xinjiang. It sold Hetian jade, which had the characteristics of assured quality and guaranteed after-sales (no reason to return or exchange within 100 days). In addition, there was a well-known jewelry and jade shop like De Yuan Xing. The old shopkeeper, Tie Bao Ting, had a unique experience. When choosing a jade store, there were many factors to consider. For example, some merchants in some areas might have some problems, such as some jade stores in Xinjiang. Because there were many experienced players in the local area, it might be difficult for laymen to choose good materials; The local return of materials led to a high price; The cost of clothing, food, accommodation and transportation was high if you went to buy; Moreover, it was difficult to distinguish between real and fake jade, and there might be fake methods in the place of origin. Many good jade materials would be shipped to Suzhou, Henan and other places for processing and sales. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>

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2026-08-25 05:55

How can I look at the celebrity concert program list?

You can check the celebrity concert program list in the following ways: 1. ** Official ticketing platform **: For example, the Inner Mongolia ticketing website. The official platform for purchasing tickets may publish information related to the program list. 2. ** Official Information Channel **: For example, the official website, official Weibo, official TikTok account, etc. Artists or concert organizers will publish information related to the program list on these official information channels. 3. ** News media reports **: For example, headlines, search engine news, etc. Reporters may obtain information about the concert program list and report it. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>

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2026-08-25 05:55

Harry Potter and Ginny

Bonnie Wright, who played Ginny in Harry Potter, had a low-key wedding with the American businessman Andrew Rococo on March 21, 2022. She announced her pregnancy on April 29, 2023, and after giving birth in 2024, she showed cliff-like aging and wrinkles all over her face. Harry Potter and the Order of the Phoenix is not enough. Please click to read the novel!

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2026-08-25 05:55

Shangguan Rao's latest novel

According to the information provided, Shangguan Rao's " Love Like Dust, Heart Towards Water " and " Singing to the Moon, Drunken Life " were the CEO's novels, but it was impossible to determine which one was her latest novel. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>

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2026-08-25 05:54

What is the normal reaction of a girl chatting with you?

There were many normal reactions when a girl chatted with you. In terms of eye contact, they might look at you normally, but there would be no special affection or deliberate evasion. Eye contact was more natural and peaceful. Judging from the content of the conversation, she would normally express her views, thoughts, or share some ordinary experiences. There would not be excessive coquettishness or ambiguous hints. For example, they would talk about their daily studies, work, hobbies, and other topics like ordinary friends. They would not deliberately explore the deeper or private parts of their private life. In terms of emotional reactions, there would be no excessive shyness or blushing. The smile was also a normal and polite smile, not the kind of smile that could not be suppressed when he saw someone he liked. At the same time, there would be no obvious nervousness, and his body movements would be more natural and relaxed. He would not deliberately approach or avoid physical contact. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>

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2026-08-25 05:54
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