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‫Welcome back.

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‫Today, we're going to talk about an interesting category of mattresses which are called also normal

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‫mattresses or the normal mattresses are mattresses whose inverse equals their transpose.

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‫So normally, if we have a matrix, a then it's inverse would be a superscript minus one.

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‫And it has to follow this relationship a times.

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‫A inverse equals a inverse times A equals ie, which is the identity matrix.

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‫For example, a 3-D identity matrix looks like this.

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‫You have three ones here in the diagonal and the rest of the elements are zeros.

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‫It's like one when we work with scalars.

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‫However, if A is also an author normal matrix, then a inverse equals a transposed.

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‫Therefore you can say that a times a transposed equals a transposed times A equals the identity matrix.

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‫Now the thing is that our three rotation matrices that we had derived in the previous videos are also

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‫also normal matrices.

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‫Because of that fact, it is very easy for you to find their inverses.

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‫So to find the inverse of our sub X are sub Y and our Sabzi, which are the rotation matrices about

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‫their respective axes, you just need to take their transpose.

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‫So here's another exercise for you.

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‫Find the inverse of these three rotation matrices and you will see the solution in the next video.

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‫See you there.