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How do you solve a matrix equation using the
... In the previous question, we wrote systems of equations as a matrix equation AX B . In this format, the matrix A contains the coefficients on the variables, matrix X contains the variables, and matrix B contains the constants. Solving the system of equations means that we need to solve for the var ...
... In the previous question, we wrote systems of equations as a matrix equation AX B . In this format, the matrix A contains the coefficients on the variables, matrix X contains the variables, and matrix B contains the constants. Solving the system of equations means that we need to solve for the var ...
Whitman-Hanson Regional High School provides all students with a
... A matrix element is identified by its position. Write the row number first and then the column number. 5. How is it determined whether two matrices are equal? Two matrices are equal if an only if they have the same dimensions and their corresponding elements are equal. 6. What is meant by correspond ...
... A matrix element is identified by its position. Write the row number first and then the column number. 5. How is it determined whether two matrices are equal? Two matrices are equal if an only if they have the same dimensions and their corresponding elements are equal. 6. What is meant by correspond ...
paper - Math TAMU
... THEOREM 4. The algorithm SNF is polynomial. Proof. Note that for a fixed every time Step 4 or 5 is passed Ai+l,i+ is replaced by a proper divisor of itself except the last and possibly the first times. Thus, for a fixed i, Steps 4 and 5 are executed at most log I[A(i)ll + 2 times where A(i) denotes ...
... THEOREM 4. The algorithm SNF is polynomial. Proof. Note that for a fixed every time Step 4 or 5 is passed Ai+l,i+ is replaced by a proper divisor of itself except the last and possibly the first times. Thus, for a fixed i, Steps 4 and 5 are executed at most log I[A(i)ll + 2 times where A(i) denotes ...
Matrices - bscsf13
... The elements of a matrix also have names, usually a lowercase letter the same as the matrix name, with the position of the element written as a subscript. So, for example, the 3x3 matrix A might be written as: Sometimes you write A = [aij] to say that the elements of matrix A are named aij. ...
... The elements of a matrix also have names, usually a lowercase letter the same as the matrix name, with the position of the element written as a subscript. So, for example, the 3x3 matrix A might be written as: Sometimes you write A = [aij] to say that the elements of matrix A are named aij. ...
Jordan normal form
In linear algebra, a Jordan normal form (often called Jordan canonical form)of a linear operator on a finite-dimensional vector space is an upper triangular matrix of a particular form called a Jordan matrix, representing the operator with respect to some basis. Such matrix has each non-zero off-diagonal entry equal to 1, immediately above the main diagonal (on the superdiagonal), and with identical diagonal entries to the left and below them. If the vector space is over a field K, then a basis with respect to which the matrix has the required form exists if and only if all eigenvalues of the matrix lie in K, or equivalently if the characteristic polynomial of the operator splits into linear factors over K. This condition is always satisfied if K is the field of complex numbers. The diagonal entries of the normal form are the eigenvalues of the operator, with the number of times each one occurs being given by its algebraic multiplicity.If the operator is originally given by a square matrix M, then its Jordan normal form is also called the Jordan normal form of M. Any square matrix has a Jordan normal form if the field of coefficients is extended to one containing all the eigenvalues of the matrix. In spite of its name, the normal form for a given M is not entirely unique, as it is a block diagonal matrix formed of Jordan blocks, the order of which is not fixed; it is conventional to group blocks for the same eigenvalue together, but no ordering is imposed among the eigenvalues, nor among the blocks for a given eigenvalue, although the latter could for instance be ordered by weakly decreasing size.The Jordan–Chevalley decomposition is particularly simple with respect to a basis for which the operator takes its Jordan normal form. The diagonal form for diagonalizable matrices, for instance normal matrices, is a special case of the Jordan normal form.The Jordan normal form is named after Camille Jordan.