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What is the importance of a dot product being equal to zero?
Vectors are said to be orthogonal if their dot product is zero.Vectors in Rn are perpendicular if they are nonzero and orthogonal.
If the product of two matrices is the identity matrix they are?
If the product of two matrices is the identity matrix then one matrix is the inverse or reciprocal of the other matrix. EXAMPLE A =(4 1) A-1 = (0.3 -0.1) then AA-1 = (1 0) .....(2 3)......... (-0.2 0.4)................... (1 1) The dots simply maintain the spacing and serve no other purpose.
Is the product of two elementry matrices is an elementry matrix?
No, it is not.
What is the difference between orthogonal and orthonormal vectors?
All vectors that are perpendicular (their dot product is zero) are orthogonal vectors.Orthonormal vectors are orthogonal unit vectors. Vectors are only orthonormal if they are both perpendicular have have a length of 1.
The product of two upper triangular matrices is upper triangular?
yes it is
If A is an orthogonal matrix then why is it's inverse also orthogonal?
First let's be clear on the definitions.A matrix M is orthogonal if MT=M-1Or multiply both sides by M and you have1) M MT=Ior2) MTM=IWhere I is the identity matrix.So our definition tells us a matrix is orthogonal if its transpose equals its inverse or if the product ( left or right) of the the matrix and its transpose is the identity.Now we want to show why the inverse of an orthogonal matrix is also orthogonal.Let A be orthogonal. We are assuming it is square since it has an inverse.Now we want to show that A-1 is orthogonal.We need to show that the inverse is equal to the transpose.Since A is orthogonal, A=ATLet's multiply both sides by A-1A-1 A= A-1 ATOr A-1 AT =ICompare this to the definition above in 1) (M MT=I)do you see how A-1 now fits the definition of orthogonal?Or course we could have multiplied on the left and then we would have arrived at 2) above.
What is the importance of a dot product being equal to zero?
Vectors are said to be orthogonal if their dot product is zero.Vectors in Rn are perpendicular if they are nonzero and orthogonal.
These matrices represent the coordinates of two figures in the plane. Is the product of these matrices defined Answer yes or no?
no
If the product of two matrices is the identity matrix they are?
If the product of two matrices is the identity matrix then one matrix is the inverse or reciprocal of the other matrix. EXAMPLE A =(4 1) A-1 = (0.3 -0.1) then AA-1 = (1 0) .....(2 3)......... (-0.2 0.4)................... (1 1) The dots simply maintain the spacing and serve no other purpose.
Is the product of a number and its multiplicative inverse always a rational number?
If the multiplicative inverse exists then, by definition, the product is 1 which is rational.
Is the product of two elementry matrices is an elementry matrix?
No, it is not.
What are the differences between the Kronecker product and the tensor product?
The Kronecker product is a specific type of tensor product that is used for matrices, while the tensor product is a more general concept that can be applied to vectors, matrices, and other mathematical objects. The Kronecker product combines two matrices to create a larger matrix, while the tensor product combines two mathematical objects to create a new object with specific properties.
What is a word using the root word ortho?
Three of them are "orthogonal", "orthodontist", and "orthopedic", and "orthogonal" is a very important word in mathematics. For one example, two vectors are orthogonal whenever their dot product is zero. "Orthogonal" also comes into play in calculus, such as in Fourier Series.
What is the difference between orthogonal and orthonormal vectors?
All vectors that are perpendicular (their dot product is zero) are orthogonal vectors.Orthonormal vectors are orthogonal unit vectors. Vectors are only orthonormal if they are both perpendicular have have a length of 1.
The product of two upper triangular matrices is upper triangular?
yes it is
What is orthogonal?
In mathematics, "orthogonal" means perpendicular or independent. In linear algebra, vectors are orthogonal if their dot product is zero, indicating they are at right angles to each other. In statistics, orthogonal variables are uncorrelated, making them useful for multi-variable analysis.
How do you describe a product matrix without multiplying?
You can indicate the multiplication with a multiplication sign. If your matrices are "A" and "B", the product is: A x B In other words, you are indicating the product, but not actually carrying out any multiplication. Anybody who understands about matrices should know what this refers to.
