What is the expression of Cauchy s inequality?

The general proofs of Cauchy's inequality are as follows:

The formal way to write the cauchy inequality is: remember that the two columns of numbers are ai and bi, then there is.

ai^2)bi^2)

aibi)^2.

We order. f(x)(aix

bi)^2∑bi^2)x^2

aibi)x∑ai^2)

then we know that there is eternity. f(x)

With quadratic functions, there is no real root or only one real root condition.

aibi)^2

ai^2)bi^2)

So the move came to a conclusion.

Vectors as proof.

m=(a1,a2...an)

n=(b1,b2...bn)

mn=a1b1+a2b2+..anbn=(a1^2+a2^2+..an 2) (1 2) multiplied by (b1 2+b2 2+...bn 2) (1 2) multiplied by cosx

Because cosx is less than or equal to 1, so: a1b1+a2b2+.ANBN is less than or equal to A1 2+A2 2+...an 2) (1 2) multiplied by (b1 2+b2 2+...bn^2)^(1/2)

This proves the inequality

There are many more types of Cauchy inequalities, but here are only two of the more commonly used ones

Cauchy inequalityThe general form of the statement is as follows:

Mathematical Analysis, Probability Theory.

It is considered one of the most important inequalities in mathematics.

Basic introduction. Cauchy Augustin-Louis (1789-1857), a French mathematician, was born on August 21, 1789 in Paris, the son of Louis François Cauchy, a French Bourbon dynasty.

**, has been holding public office in the political maelstrom of turmoil in France. For family reasons, Cauchy himself belonged to the orthodox faction of the Bourbon dynasty and was a devout Catholic feaster.

His foundation in pure mathematics and applied mathematics is quite profound, and many mathematical theorems and formulas are called by his name, such as Cauchy inequality and Cauchy integral formula. In mathematical writing, he is considered to be second only to Euler in quantity.

1821) and "Report on the Theory of Definite Integrals" (1827) are the most famous.

Cauchy's inequality (cauchy's inequality) is an important inequality relation in mathematics that describes the product of vectors in the inner product space.

In high school math, the Cauchy inequality can be expressed as:

a b +a squire b +a b )|a₁² a₂² aₙ²)b₁² b₂² bₙ²)

where a, a, a, and b, b, b are real or complex numbers.

This inequality states that the absolute value of the product of two vectors will not be greater than the product of the square roots of the product of their respective modulos. In other words, the absolute value of the product of the two vectors trapped will not exceed the product of their lengths.

This inequality has a wide range of applications in various branches of mathematics, including linear algebra, real analysis, probability theory, and more. It is one of the basic inequalities in mathematics and has important theoretical and practical significance.

What is the Cauchy inequality in high school mathematics, I believe that many Tongxiang Yuanxue want to know, today we will talk about this topic. Cauchy's inequality is an important inequality in mathematics, which was discovered by the French mathematician Cauchy in the middle of the 19th century. This inequality is of great significance for the study of mathematical problems, so let's take a look at its specific applications.

First of all, Cauchy inequality is very widely used in the study of functions. For example, if we study the monotonicity of a function, if the Cauchy inequality of the function is true, then it means that the parity of the function is different, so that we can judge the parity of the function by this inequality.

Secondly, Cauchy's inequality is also widely used in geometry. For example, if we study the tangent equation of a curve, if the Cauchy inequality is true, then it means that the tangent of the curve is oblique, so that we can judge the tangent equation of the curve by this inequality.

Finally, Cauchy's inequality is also very widely used in statistics. For example, if we study the distribution of a data, if the Cauchy inequality holds, then it means that the distribution of the data is discrete, so that we can judge the distribution of the data through this inequality.

In conclusion, Cauchy's inequality is very widely used in mathematics, and it is a very important inequality in mathematics. If you want to know more about Cauchy's inequality, you can **** the channel, and we will continue to bring you more mathematical knowledge.