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I assume you mean covariance matrix and I assume that you are familiar with the definition:
C = E[(X-u)(X-u)T]
where X is a random vector and u = E(X) is the mean
The definition of non-negative definite is:
xTCx ≥ 0 for any vector x Є R
So is xTE[(X-u)(X-u)T]x ≥ 0?
Then, from one of the covariance properties:
E[(xT(X-u))((X-u)Tx)] = E[xT([(X-u)(X-u)T]x)] = E[((xTI)x)] = E[xTx]
Finally, since we've already defined x to have only real values, xTx is therefore non-negative definite by definition.
What else can I help you with?
Which of the SmartArt graphic types show relationships of parts to a whole?
matrix
What does a correlation matrix show?
A correlation matrix is a table that displays the correlation coefficients between multiple variables, providing a summary of their pairwise relationships. Each cell in the matrix represents the strength and direction of the linear relationship between two variables, typically ranging from -1 to 1. A value close to 1 indicates a strong positive correlation, while a value close to -1 indicates a strong negative correlation. Values around 0 suggest little to no correlation.
To show the variation in a set of data you could calculate the what?
To show the variation in a set of data, you could calculate the standard deviation, which measures the dispersion or spread of the data points around the mean. Additionally, you might consider calculating the variance, which is the square of the standard deviation. Other measures, such as the range or interquartile range, can also provide insights into the variability within the dataset.
Show some details about the set of all orthogonal matrices?
The set of all orthogonal matrices consists of square matrices ( Q ) that satisfy the condition ( Q^T Q = I ), where ( Q^T ) is the transpose of ( Q ) and ( I ) is the identity matrix. This means that the columns (and rows) of an orthogonal matrix are orthonormal vectors. Orthogonal matrices preserve the Euclidean norm of vectors and the inner product, making them crucial in various applications such as rotations and reflections in geometry. The determinant of an orthogonal matrix is either ( +1 ) or ( -1 ), corresponding to special orthogonal matrices (rotations) and improper orthogonal matrices (reflections), respectively.
How do you show that a square matrix A is similar to its transpose?
First we will handle the diagonalizable case.Assume A is diagonalizable, A=VDV-1.Thus AT=(V-1)TDVT,and D= VT AT(V-1)T.Finally we have that A= VVT AT(V-1)TV-1, hence A is similar to ATwith matrix VVT.If A is not diagonalizable, then we must consider its Jordan canonical form,A=VJV-1, where J is block diagonal with Jordan blocks along the diagonal.Recall that a Jordan block of size m with eigenvalue at L is a mxm matrix having L along the diagonal and ones along the superdiagonal.A Jordan block is similar to its transpose via the permutation that has ones along the antidiagonal, and zeros elsewhere.With this in mind we proceed as in the diagonalizable case,AT=(V-1)TJTVT.There exists a block diagonal permutation matrix P such thatJT=PJPT, thus J=PTVT AT(V-1)TP.Finally we have that A= VPTVT AT(V-1)TPV-1, hence A is similar to ATwith matrix VPTVT.Q.E.D.
How prove that variance-covariance matrix is nonnegative definite?
To prove that the variance-covariance matrix ( \Sigma ) is nonnegative definite, we can show that for any vector ( x ), the quadratic form ( x^T \Sigma x \geq 0 ). The variance-covariance matrix is defined as ( \Sigma = E[(X - E[X])(X - E[X])^T] ), where ( X ) is a random vector. By substituting ( x^T \Sigma x ) and using the properties of expected values and the definition of variance, we find that the expression equals the variance of the linear combination of the components of ( X ), which is always nonnegative. Thus, ( \Sigma ) is nonnegative definite.
Show that in simple random sampling the sample variance is an unbiased estimator of population variance?
It is a biased estimator. S.R.S leads to a biased sample variance but i.i.d random sampling leads to a unbiased sample variance.
Show how the data set as a whole is spread around the mean?
I think the answer is variance
Show me matrix of distance region 12?
that is not a ?
Let A be a 6by4 matrix and B a 4by6 matrix show that the 6by6 matrix AB can not be invertible?
It is not possible to show that since it is not necessarily true.There is absolutely nothing in the information that is given in the question which implies that AB is not invertible.
Show that for a square matrix the linear dependence of the row vectors implies that of the column vectors and conversely.?
show that SQUARE MATRIX THE LINEAR DEPENDENCE OF THE ROW VECTOR?
A matrix SmartArt can be used to show connection?
nope
Which SmartArt graphic can be used to show a timeline?
Matrix
How do you show a matrix is invertible?
For small matrices the simplest way is to show that its determinant is not zero.
Did Neo die in The Matrix?
no. in the film the show him looking up.
Which of the SmartArt graphic types show relationships of parts to a whole?
matrix
Which of the smartArt graphic type show relationships of parts to a whole?
matrix
