V be a ?nite-dimensional inner product space over f

Reference no: EM13869942

6. Give an orthonormal basis for null(T), where T∈L(C4) is the map with canonical matrix

1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1

6. Let V be a ?nite-dimensional inner product space over F, and let U be a subspace of V. Prove that the orthogonal complement U⊥ of Uwith respect to the inner product ?⋅,⋅? on V satis?es

dim(U⊥)=dim(V)-dim(U).

7. Let V be a ?nite-dimensional inner product space over F, and let U be a subspace of V. Prove that U=V if and only if the orthogonal complement U⊥ of U with respect to the inner product ?⋅,⋅? on V satis?es U⊥={0}.

10. Prove or give a counterexample: The Gram-Schmidt process applied to an an orthonormal list of vectors reproduces that list unchanged.

(Prove by induction)

Reference no: EM13869942

Questions Cloud

How are outsourcing and vertical integration related : How are outsourcing and vertical integration related? Can a single firm successfully do both? The Winfield Distributing Company has maintained an 80% service level policy for inventory of string trimmers. Mean demand during lead time is 170 trimmer..

What proportion of the tires will need to be replaced : If the manufacturer guarantees the tread life of the tires for the first 53,520 miles, what proportion of the tires will need to be replaced under warranty?

What is the probability that a particular flight may be safe : What is the probability that a particular flight may be safe with at least one working radio? Why does the usual rounding rule of three significant digits not work here? Is this probability high enough to ensure flight safety?

How do you define training : How do you define training? How do you define professional development? What are the most common characteristics of an effective training and development program

V be a ?nite-dimensional inner product space over f : Let V be a ?nite-dimensional inner product space over F, and let U be a subspace of V. Prove that the orthogonal complement U⊥ of Uwith respect to the inner product ?⋅,⋅? on V satis?es dim(U⊥)=dim(V)-dim(U).

A supremum or have infinite supremum : 1). A number of sets do not have a supremum or have infinite supremum. do the same two statements?

Three machines turn out all the products in a factory : Three machines turn out all the products in a factory, with the first machine producing25%of the products, the second machine10%, and the third machine65%. The first machine produces defective products3%of the time, the second machine2%of the time an..

Can you conclude that the mean times are different : At a significance level of 0.01, can you conclude that the mean times are different? Assume each population of relief times is normally distributed and that the population variances are equal.

Determine the multiple coefficient of determination : At alpha = 0.05, test to see if the coefficient of x1 is significantly different from zero. Determine the multiple coefficient of determination.

User Account

All Pages